In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity...In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.展开更多
The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional ...The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurs...We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown parameters.We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator.We also introduce alternative estimators,which can be looked upon as an application of the least squares estimator.In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.展开更多
Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a c...Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.展开更多
An initial value boundary problem for system of diffusion equations with delay arguments and dynamic nonlinear boundary conditions is considered. The problem describes evolution of the carrier density and the radiatio...An initial value boundary problem for system of diffusion equations with delay arguments and dynamic nonlinear boundary conditions is considered. The problem describes evolution of the carrier density and the radiation density in the semiconductor laser or laser diodes with “memory” and with feedback. It is shown that the boundary problem can be reduced to a system of difference equations with continuous time. For large times, solutions of these equations tend to piecewise constant asymptotic periodic wave functions which represent chain of shock waves with finite or infinite points of discontinuities on a period. Applications to the optical systems with linear media and nonlinear surface optical properties with feedback have been done. The results are compared with the experiment.展开更多
Cui and Zhong(2019),(Computational Statistics&Data Analysis,139,117–133)proposed a test based on the mean variance(MV)index to test independence between a categorical random variable Y with R categories and a con...Cui and Zhong(2019),(Computational Statistics&Data Analysis,139,117–133)proposed a test based on the mean variance(MV)index to test independence between a categorical random variable Y with R categories and a continuous random variable X.They ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity,which brings many merits to the MV test,including making it more convenient for independence testing when R is large.This paper considers a new test called the integral Pearson chi-square(IPC)test,whose test statistic can be viewed as a modified MV test statistic.A central limit theorem of the martin-gale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution,rendering the IPC test sharing many merits with the MV test.As an application of such a theoretical finding,the IPC test is extended to test independence between continuous random variables.The finite sample performance of the proposed test is assessed by Monte Carlo simulations,and a real data example is presented for illustration.展开更多
Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of in...Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.展开更多
Nowadays,researchers are frequently confronted with challenges from massive data computing by a number of limitations of computer primary memory.Modal regression(MR)is a good alternative of the mean regression and lik...Nowadays,researchers are frequently confronted with challenges from massive data computing by a number of limitations of computer primary memory.Modal regression(MR)is a good alternative of the mean regression and likelihood based methods,because of its robustness and high efficiency.To this end,the authors extend MR to massive data analysis and propose a computationally and statistically efficient divide and conquer MR method(DC-MR).The major novelty of this method consists of splitting one entire dataset into several blocks,implementing the MR method on data in each block,and deriving final results through combining these regression results via a weighted average,which provides approximate estimates of regression results on the entire dataset.The proposed method significantly reduces the required amount of primary memory,and the resulting estimator is theoretically as efficient as the traditional MR on the entire data set.The authors also investigate a multiple hypothesis testing variable selection approach to select significant parametric components and prove the approach possessing the oracle property.In addition,the authors propose a practical modified modal expectation-maximization(MEM)algorithm for the proposed procedures.Numerical studies on simulated and real datasets are conducted to assess and showcase the practical and effective performance of our proposed methods.展开更多
Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new te...Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new test procedures for testing mean vector in large dimension and small samples.We do not focus on the mean vector directly,which is a different framework from the existing choices.The first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample size.The second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to infinity.Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.展开更多
The statistical inference of the Vasicek model driven by small Levy process has a long history.In this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_...The statistical inference of the Vasicek model driven by small Levy process has a long history.In this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_0,driven by small fractional Lévy noise with the known parameter d less than one half,based on discrete high-frequency observations at regularly spaced time points{t_i=i/n,i=1,2,...,n}.For the general case and the null recurrent case,the consistency as well as the asymptotic behavior of least squares estimation of unknown parametersμandθhave been established as small dispersion coefficientε→0 and large sample size n→∞simultaneously.展开更多
Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the...Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.展开更多
In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula-tions are in simple tree...In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula-tions are in simple tree order. We provide an asymptotic represen-tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be n-consistent and asymptotically normal under appropriate con-ditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.展开更多
One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality...One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.展开更多
VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asympt...VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.展开更多
New technological advancements combined with powerful computer hardware and high-speed network make big data available.The massive sample size of big data introduces unique computational challenges on scalability and ...New technological advancements combined with powerful computer hardware and high-speed network make big data available.The massive sample size of big data introduces unique computational challenges on scalability and storage of statistical methods.In this paper,we focus on the lack of fit test of parametric regression models under the framework of big data.We develop a computationally feasible testing approach via integrating the divide-and-conquer algorithm into a powerful nonparametric test statistic.Our theory results show that under mild conditions,the asymptotic null distribution of the proposed test is standard normal.Furthermore,the proposed test benefits fromthe use of data-driven bandwidth procedure and thus possesses certain adaptive property.Simulation studies show that the proposed method has satisfactory performances,and it is illustrated with an analysis of an airline data.展开更多
A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments.It is shown that the asympto...A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments.It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameterfree,but χ_(1)^(2) is a conservative asymptotic null distribution.A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability.An example from an animal clinical trial is discussed.展开更多
We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions f...We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.展开更多
基金supported by the National Natural Science Foundation of China(12131015,12071422)。
文摘In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.
基金Key Natural Science Foundation of Anhui Education Commission,China(No.KJ2017A568)Natural Science Foundation of Anhui Province,China(No.1808085MA02)+1 种基金Quality Engineering Project of Anhui Province,China(No.2019jyxm0476)Quality Engineering Project of Bengbu University,China(No.2018JYXML8)。
文摘The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
基金supported by National Natural Science Foundation of China(12071003).
文摘We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes dY_(s)=(∑_(j=1)^(k)μ_(j)φ_(j)(s)-βY_(s))ds+dZ_(s)^(q,H),driven by the Hermite process Z_(s)^(q,H)with order q≥1 and a Hurst index H∈(1/2,1),where the periodic functionsφ_(j)(s),,j=1,...,κare bounded,and the real numbersμ_(j),,j=1,...,κtogether withβ>0 are unknown parameters.We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator.We also introduce alternative estimators,which can be looked upon as an application of the least squares estimator.In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean,our work can be regarded as its non-Gaussian extension.
文摘Consider a distribution with several parameters whose exact values are unknown and need to be estimated using the maximum-likelihood technique. Under a regular case of estimation, it is fairly routine to construct a confidence region for all such parameters, based on the natural logarithm of the corresponding likelihood function. In this article, we investigate the case of doing this for only some of these parameters, assuming that the remaining (so called nuisance) parameters are of no interest to us. This is to be done at a chosen level of confidence, maintaining the usual accuracy of this procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it by many explicit examples.
文摘An initial value boundary problem for system of diffusion equations with delay arguments and dynamic nonlinear boundary conditions is considered. The problem describes evolution of the carrier density and the radiation density in the semiconductor laser or laser diodes with “memory” and with feedback. It is shown that the boundary problem can be reduced to a system of difference equations with continuous time. For large times, solutions of these equations tend to piecewise constant asymptotic periodic wave functions which represent chain of shock waves with finite or infinite points of discontinuities on a period. Applications to the optical systems with linear media and nonlinear surface optical properties with feedback have been done. The results are compared with the experiment.
基金National Natural Science Foundation of China[Grant numbers 12271286,11931001 and 11771241].
文摘Cui and Zhong(2019),(Computational Statistics&Data Analysis,139,117–133)proposed a test based on the mean variance(MV)index to test independence between a categorical random variable Y with R categories and a continuous random variable X.They ingeniously proved the asymptotic normality of the MV test statistic when R diverges to infinity,which brings many merits to the MV test,including making it more convenient for independence testing when R is large.This paper considers a new test called the integral Pearson chi-square(IPC)test,whose test statistic can be viewed as a modified MV test statistic.A central limit theorem of the martin-gale difference is used to show that the asymptotic null distribution of the standardized IPC test statistic when R is diverging is also a normal distribution,rendering the IPC test sharing many merits with the MV test.As an application of such a theoretical finding,the IPC test is extended to test independence between continuous random variables.The finite sample performance of the proposed test is assessed by Monte Carlo simulations,and a real data example is presented for illustration.
基金partially supported by Beijing Natural Science Foundation under Grant No.Z180006.
文摘Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.
基金supported by the Fundamental Research Funds for the Central Universities under Grant No.JBK1806002the National Natural Science Foundation of China under Grant No.11471264。
文摘Nowadays,researchers are frequently confronted with challenges from massive data computing by a number of limitations of computer primary memory.Modal regression(MR)is a good alternative of the mean regression and likelihood based methods,because of its robustness and high efficiency.To this end,the authors extend MR to massive data analysis and propose a computationally and statistically efficient divide and conquer MR method(DC-MR).The major novelty of this method consists of splitting one entire dataset into several blocks,implementing the MR method on data in each block,and deriving final results through combining these regression results via a weighted average,which provides approximate estimates of regression results on the entire dataset.The proposed method significantly reduces the required amount of primary memory,and the resulting estimator is theoretically as efficient as the traditional MR on the entire data set.The authors also investigate a multiple hypothesis testing variable selection approach to select significant parametric components and prove the approach possessing the oracle property.In addition,the authors propose a practical modified modal expectation-maximization(MEM)algorithm for the proposed procedures.Numerical studies on simulated and real datasets are conducted to assess and showcase the practical and effective performance of our proposed methods.
文摘Several tests for multivariate mean vector have been proposed in the recent literature.Generally,these tests are directly concerned with the mean vector of a high-dimensional distribution.The paper presents two new test procedures for testing mean vector in large dimension and small samples.We do not focus on the mean vector directly,which is a different framework from the existing choices.The first test procedure is based on the asymptotic distribution of the test statistic,where the dimension increases with the sample size.The second test procedure is based on the permutation distribution of the test statistic,where the sample size is fixed and the dimension grows to infinity.Simulations are carried out to examine the finite-sample performance of the tests and to compare them with some popular nonparametric tests available in the literature.
基金Supported by the Distinguished Young Scholars Foundation of Anhui Province(Grant No.1608085J06)Top Talent Project of University Discipline(speciality)(Grant No.gxbj ZD03)the National Natural Science Foundation of China(Grant No.11901005)。
文摘The statistical inference of the Vasicek model driven by small Levy process has a long history.In this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_0,driven by small fractional Lévy noise with the known parameter d less than one half,based on discrete high-frequency observations at regularly spaced time points{t_i=i/n,i=1,2,...,n}.For the general case and the null recurrent case,the consistency as well as the asymptotic behavior of least squares estimation of unknown parametersμandθhave been established as small dispersion coefficientε→0 and large sample size n→∞simultaneously.
基金Beijing Natural Science Foundation(Grant No.Z200001)National Natural Science Foundation of China(Grant Nos.11871001,11971478 and 11971001)the Fundamental Research Funds for the Central Universities(Grant No.2019NTSS18)。
文摘Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.
基金Supported by the National Natural Science Foundation of China (10771163)
文摘In this paper, we consider testing the hypothesis that all multinomial populations in the stratified contingency table are identically distributed against the alternative that all these popula-tions are in simple tree order. We provide an asymptotic represen-tation of the order-restricted maximum likelihood estimate of the unknown parameters. The resulting estimators are proven to be n-consistent and asymptotically normal under appropriate con-ditions. A chi-squared test method is used for this hypothesis test problem. A real data set is applied to illustrate our theoretical result.
文摘One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.
基金Guangjun Shen was supported by the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)the Top Talent Project of University Discipline(speciality)(Grant No.gxbjZD03)+2 种基金the National Natural Science Foundation of China(Grant No.11901005)Qian Yu was supported by the ECNU Academic Innovation Promotion Program for Excellent Doctoral Students(YBNLTS2019-010)the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management(2018FEM-BCKYB014).
文摘VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.
基金This paper was supported by the National Natural Science Foundation of China[grant number 11431006][grant num-ber 11690015]+1 种基金[grant number 11371202][grant number 11622104].
文摘New technological advancements combined with powerful computer hardware and high-speed network make big data available.The massive sample size of big data introduces unique computational challenges on scalability and storage of statistical methods.In this paper,we focus on the lack of fit test of parametric regression models under the framework of big data.We develop a computationally feasible testing approach via integrating the divide-and-conquer algorithm into a powerful nonparametric test statistic.Our theory results show that under mild conditions,the asymptotic null distribution of the proposed test is standard normal.Furthermore,the proposed test benefits fromthe use of data-driven bandwidth procedure and thus possesses certain adaptive property.Simulation studies show that the proposed method has satisfactory performances,and it is illustrated with an analysis of an airline data.
基金partially supported by the National Institutes of Health(NIH)grant R01-GM085205A1partially supported by the National Science Foundation(NSF)grant SES-1118469partially supported by the National Science Foundation(NSF)grant SES-1121794.
文摘A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments.It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameterfree,but χ_(1)^(2) is a conservative asymptotic null distribution.A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability.An example from an animal clinical trial is discussed.
基金Project supported by the National Natural Science Foundation of China(Nos.61873284,61473315,and 61321003)。
文摘We investigate the stability of Boolean networks(BNs)with impulses triggered by both states and random factors.A hybrid index model is used to describe impulsive BNs.First,several necessary and sufficient conditions for forward completeness are obtained.Second,based on the stability criterion of probabilistic BNs and the forward completeness criterion,the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented.The relationship between these two kinds of stability is discussed.Last,examples and time-domain simulations are provided to illustrate the obtained results.
