This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation ...This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.展开更多
Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We pr...Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We propose a joint PP-PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion.A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data,the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion,low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness,and a fast algorithm is used to solve the objective function while minimizing the computational load.The proposed method has superior antinoising properties and well reproduces real data.展开更多
This paper addresses the generalized linear complementarity problem （GLCP） over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over...This paper addresses the generalized linear complementarity problem （GLCP） over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method.展开更多
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether＇s theorem and the Noether＇s inverse theorem for generalized linear nonholonomic mechanical systems ar...By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether＇s theorem and the Noether＇s inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.展开更多
We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, i...We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.展开更多
In a linear regression model, testing for uniformity of the variance of the residuals is a significant integral part of statistical analysis. This is a crucial assumption that requires statistical confirmation via the...In a linear regression model, testing for uniformity of the variance of the residuals is a significant integral part of statistical analysis. This is a crucial assumption that requires statistical confirmation via the use of some statistical tests mostly before carrying out the Analysis of Variance (ANOVA) technique. Many academic researchers have published series of papers (articles) on some tests for detecting variance heterogeneity assumption in multiple linear regression models. So many comparisons on these tests have been made using various statistical techniques like biases, error rates as well as powers. Aside comparisons, modifications of some of these statistical tests for detecting variance heterogeneity have been reported in some literatures in recent years. In a multiple linear regression situation, much work has not been done on comparing some selected statistical tests for homoscedasticity assumption when linear, quadratic, square root, and exponential forms of heteroscedasticity are injected into the residuals. As a result of this fact, the present study intends to work extensively on all these areas of interest with a view to filling the gap. The paper aims at providing a comprehensive comparative analysis of asymptotic behaviour of some selected statistical tests for homoscedasticity assumption in order to hunt for the best statistical test for detecting heteroscedasticity in a multiple linear regression scenario with varying variances and levels of significance. In the literature, several tests for homoscedasticity are available but only nine: Breusch-Godfrey test, studentized Breusch-Pagan test, White’s test, Nonconstant Variance Score test, Park test, Spearman Rank, <span>Glejser test, Goldfeld-Quandt test, Harrison-McCabe test were considered for this study;this is with a view to examining, by Monte Carlo simulations, their</span><span> asymptotic behaviours. However, four different forms of heteroscedastic structures: exponential and linear (generalize of square-root and quadratic structures) were injected into the residual part of the multiple linear regression models at different categories of sample sizes: 30, 50, 100, 200, 500 and 1000. Evaluations of the performances were done within R environment. Among other findings, our investigations revealed that Glejser and Park tests returned the best test to employ to check for heteroscedasticity in EHS and LHS respectively also White and Harrison-McCabe tests returned the best test to employ to check for homoscedasticity in EHS and LHS respectively for sample size less than 50.</span>展开更多
Changes in climate factors such as temperature, rainfall, humidity, and wind speed are natural processes that could significantly impact the incidence of infectious diseases. Dengue is a widespread disease that has of...Changes in climate factors such as temperature, rainfall, humidity, and wind speed are natural processes that could significantly impact the incidence of infectious diseases. Dengue is a widespread disease that has often been documented when it comes to the impact of climate change. It has become a significant concern, especially for the Malaysian health authorities, due to its rapid spread and serious effects, leading to loss of life. Several statistical models were performed to identify climatic factors associated with infectious diseases. However, because of the complex and nonlinear interactions between climate variables and disease components, modelling their relationships have become the main challenge in climate-health studies. Hence, this study proposed a Generalized Linear Model (GLM) via Poisson and Negative Binomial to examine the effects of the climate factors on dengue incidence by considering the collinearity between variables. This study focuses on the dengue hot spots in Malaysia for the year 2014. Since there exists collinearity between climate factors, the analysis was done separately using three different models. The study revealed that rainfall, temperature, humidity, and wind speed were statistically significant with dengue incidence, and most of them shown a negative effect. Of all variables, wind speed has the most significant impact on dengue incidence. Having this kind of relationships, policymakers should formulate better plans such that precautionary steps can be taken to reduce the spread of dengue diseases.展开更多
The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the se...The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the setting with highly correlated covariates.In this paper,the semi-standard partial covariance(SPAC)method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates,and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions.Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.展开更多
Background Abiotic factors exert different impacts on the abundance of individual tree species in the forest but little has been known about the impact of abiotic factors on the individual plant,particularly,in a trop...Background Abiotic factors exert different impacts on the abundance of individual tree species in the forest but little has been known about the impact of abiotic factors on the individual plant,particularly,in a tropical forest.This study identified the impact of abiotic factors on the abundances of Podocarpus falcatus,Croton macrostachyus,Celtis africana,Syzygium guineense,Olea capensis,Diospyros abyssinica,Feliucium decipenses,and Coffea arabica.A systematic sample design was used in the Harana forest,where 1122 plots were established to collect the abundance of species.Random forest(RF),artificial neural network(ANN),and generalized linear model(GLM)models were used to examine the impacts of topographic,climatic,and edaphic factors on the log abundances of woody species.The RF model was used to predict the spatial distribution maps of the log abundances of each species.Results The RF model achieved a better prediction accuracy with R^(2)=71%and a mean squared error(MSE)of 0.28 for Feliucium decipenses.The RF model differentiated elevation,temperature,precipitation,clay,and potassium were the top variables that influenced the abundance of species.The ANN model showed that elevation induced a nega-tive impact on the log abundances of all woody species.The GLM model reaffirmed the negative impact of elevation on all woody species except the log abundances of Syzygium guineense and Olea capensis.The ANN model indicated that soil organic matter(SOM)could positively affect the log abundances of all woody species.The GLM showed a similar positive impact of SOM,except for a negative impact on the log abundance of Celtis africana at p<0.05.The spatial distributions of the log abundances of Coffee arabica,Filicium decipenses,and Celtis africana were confined to the eastern parts,while the log abundance of Olea capensis was limited to the western parts.Conclusions The impacts of abiotic factors on the abundance of woody species may vary with species.This ecological understanding could guide the restoration activity of individual species.The prediction maps in this study provide spatially explicit information which can enhance the successful implementation of species conservation.展开更多
Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigat...Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.展开更多
This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by util...This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.展开更多
Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for suc...Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for such territory risk classification.In this work,spatially constrained clustering is first applied to insurance loss data to form rating territories.The generalized linear model(GLM)and generalized linear mixed model(GLMM)are then proposed to derive the risk relativities of obtained clusters.Each basic rating unit within the same cluster,namely Forward Sortation Area(FSA),takes the same risk relativity value as its cluster.The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics,including RMSE,MAD,and Gini coefficients.The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.展开更多
Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-li...Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.展开更多
The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing...The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate.Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.展开更多
Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected ...Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.展开更多
In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for u...In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.展开更多
For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. U...For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of β^n展开更多
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is as...For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.展开更多
基金This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(Grant Number IMSIU-RG23142).
文摘This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.
基金supported by the 863 Program of China(No.2013AA064201)
文摘Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We propose a joint PP-PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion.A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data,the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion,low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness,and a fast algorithm is used to solve the objective function while minimizing the computational load.The proposed method has superior antinoising properties and well reproduces real data.
基金supported by National Natural Science Foundation of China (No. 10771120)
文摘This paper addresses the generalized linear complementarity problem （GLCP） over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
基金Project supported by the Natural Science Foundation of Weifang University,China(Grant No.2008Z03)
文摘By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether＇s theorem and the Noether＇s inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.
文摘We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.
文摘In a linear regression model, testing for uniformity of the variance of the residuals is a significant integral part of statistical analysis. This is a crucial assumption that requires statistical confirmation via the use of some statistical tests mostly before carrying out the Analysis of Variance (ANOVA) technique. Many academic researchers have published series of papers (articles) on some tests for detecting variance heterogeneity assumption in multiple linear regression models. So many comparisons on these tests have been made using various statistical techniques like biases, error rates as well as powers. Aside comparisons, modifications of some of these statistical tests for detecting variance heterogeneity have been reported in some literatures in recent years. In a multiple linear regression situation, much work has not been done on comparing some selected statistical tests for homoscedasticity assumption when linear, quadratic, square root, and exponential forms of heteroscedasticity are injected into the residuals. As a result of this fact, the present study intends to work extensively on all these areas of interest with a view to filling the gap. The paper aims at providing a comprehensive comparative analysis of asymptotic behaviour of some selected statistical tests for homoscedasticity assumption in order to hunt for the best statistical test for detecting heteroscedasticity in a multiple linear regression scenario with varying variances and levels of significance. In the literature, several tests for homoscedasticity are available but only nine: Breusch-Godfrey test, studentized Breusch-Pagan test, White’s test, Nonconstant Variance Score test, Park test, Spearman Rank, <span>Glejser test, Goldfeld-Quandt test, Harrison-McCabe test were considered for this study;this is with a view to examining, by Monte Carlo simulations, their</span><span> asymptotic behaviours. However, four different forms of heteroscedastic structures: exponential and linear (generalize of square-root and quadratic structures) were injected into the residual part of the multiple linear regression models at different categories of sample sizes: 30, 50, 100, 200, 500 and 1000. Evaluations of the performances were done within R environment. Among other findings, our investigations revealed that Glejser and Park tests returned the best test to employ to check for heteroscedasticity in EHS and LHS respectively also White and Harrison-McCabe tests returned the best test to employ to check for homoscedasticity in EHS and LHS respectively for sample size less than 50.</span>
文摘Changes in climate factors such as temperature, rainfall, humidity, and wind speed are natural processes that could significantly impact the incidence of infectious diseases. Dengue is a widespread disease that has often been documented when it comes to the impact of climate change. It has become a significant concern, especially for the Malaysian health authorities, due to its rapid spread and serious effects, leading to loss of life. Several statistical models were performed to identify climatic factors associated with infectious diseases. However, because of the complex and nonlinear interactions between climate variables and disease components, modelling their relationships have become the main challenge in climate-health studies. Hence, this study proposed a Generalized Linear Model (GLM) via Poisson and Negative Binomial to examine the effects of the climate factors on dengue incidence by considering the collinearity between variables. This study focuses on the dengue hot spots in Malaysia for the year 2014. Since there exists collinearity between climate factors, the analysis was done separately using three different models. The study revealed that rainfall, temperature, humidity, and wind speed were statistically significant with dengue incidence, and most of them shown a negative effect. Of all variables, wind speed has the most significant impact on dengue incidence. Having this kind of relationships, policymakers should formulate better plans such that precautionary steps can be taken to reduce the spread of dengue diseases.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001277,12271046 and 12131006)。
文摘The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the setting with highly correlated covariates.In this paper,the semi-standard partial covariance(SPAC)method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates,and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions.Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.
文摘Background Abiotic factors exert different impacts on the abundance of individual tree species in the forest but little has been known about the impact of abiotic factors on the individual plant,particularly,in a tropical forest.This study identified the impact of abiotic factors on the abundances of Podocarpus falcatus,Croton macrostachyus,Celtis africana,Syzygium guineense,Olea capensis,Diospyros abyssinica,Feliucium decipenses,and Coffea arabica.A systematic sample design was used in the Harana forest,where 1122 plots were established to collect the abundance of species.Random forest(RF),artificial neural network(ANN),and generalized linear model(GLM)models were used to examine the impacts of topographic,climatic,and edaphic factors on the log abundances of woody species.The RF model was used to predict the spatial distribution maps of the log abundances of each species.Results The RF model achieved a better prediction accuracy with R^(2)=71%and a mean squared error(MSE)of 0.28 for Feliucium decipenses.The RF model differentiated elevation,temperature,precipitation,clay,and potassium were the top variables that influenced the abundance of species.The ANN model showed that elevation induced a nega-tive impact on the log abundances of all woody species.The GLM model reaffirmed the negative impact of elevation on all woody species except the log abundances of Syzygium guineense and Olea capensis.The ANN model indicated that soil organic matter(SOM)could positively affect the log abundances of all woody species.The GLM showed a similar positive impact of SOM,except for a negative impact on the log abundance of Celtis africana at p<0.05.The spatial distributions of the log abundances of Coffee arabica,Filicium decipenses,and Celtis africana were confined to the eastern parts,while the log abundance of Olea capensis was limited to the western parts.Conclusions The impacts of abiotic factors on the abundance of woody species may vary with species.This ecological understanding could guide the restoration activity of individual species.The prediction maps in this study provide spatially explicit information which can enhance the successful implementation of species conservation.
基金supported by the Natural Science Foundation of China under Grant Nos.12031016,11061002,11801033,12071014 and 12131001the National Social Science Fund of China under Grant No.19ZDA121the Natural Science Foundation of Guangxi under Grant Nos.2015GXNSFAA139006 and LMEQF。
文摘Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.
基金the National Natural Science Foundation of China(Nos.11871196,12071133 and 12071112)the China Postdoctoral Science Foundation(No.2017M622340)+1 种基金the Key Scientific and Technological Research Projects of Henan Province(Nos.202102210147 and 192102210114)the Science and Technology Climbing Program of Henan Institute of Science and Technology(No.2018JY01).
文摘This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.
文摘Territory risk analysis has played an important role in the decision-making of auto insurance rate regulation.Due to the optimality of insurance loss data groupings,clustering methods become the natural choice for such territory risk classification.In this work,spatially constrained clustering is first applied to insurance loss data to form rating territories.The generalized linear model(GLM)and generalized linear mixed model(GLMM)are then proposed to derive the risk relativities of obtained clusters.Each basic rating unit within the same cluster,namely Forward Sortation Area(FSA),takes the same risk relativity value as its cluster.The obtained risk relativities from GLM or GLMM are used to calculate the performance metrics,including RMSE,MAD,and Gini coefficients.The spatially constrained clustering and the risk relativity estimate help obtain a set of territory risk benchmarks used in rate filings to guide the rate regulation process.
基金This work was supported by the National Natural Science Foundation of China.
文摘Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.
基金supported by the Chinese 111 Project B14019the US National Science Foundation under Grant Nos.DMS-1305474 and DMS-1612873the US National Institutes of Health Award UL1TR001412
文摘The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate.Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.
基金supported by National Natural Science Foundation of China(Grant Nos.11301569,11471029 and 11101014)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)Hong Kong Research Grant(Grant No.HKBU202711)Hong Kong Baptist University FRG Grants(Grant Nos.FRG2/11-12/110 and FRG1/13-14/018)
文摘Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.
基金supported by the President Foundation (Grant No. Y1050)the Scientific Research Foundation(Grant No. KYQD200502) of GUCAS
文摘In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.
基金Project supported by the Chinese Natural Science Foundation
文摘For generalized linear models （GLM）, in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate （MLE） β^n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of β^n
基金Project supported by the National Natural Science Foundation of China.
文摘For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
