The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint ...The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.展开更多
In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function ...In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.展开更多
Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of e...Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.展开更多
In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursiv...In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or non-recursive.Some statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild conditions.Moreover,the random weighted estimator is also investigated.Some numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.展开更多
In the case of the differential privacy under the Laplace mechanism,the asymptotic properties of parameter estimators have been derived in some special network models with common binary values,but the asymptotic prope...In the case of the differential privacy under the Laplace mechanism,the asymptotic properties of parameter estimators have been derived in some special network models with common binary values,but the asymptotic properties in network models with the ordered values are lacking.In this paper,the authors release the degree sequences of the ordered networks under a general noisy mechanism with the discrete Laplace mechanism as a special case.The authors establish the asymptotic result including the consistency and asymptotical normality of the parameter estimator when the number of parameters goes to infinity.Simulations and a real data example are provided to illustrate asymptotic results.展开更多
This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index ...This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.展开更多
The radionuclide 22Na generates the emission of a characteristic 1.275 MeVγ-ray.This is a potential astronomical observable,whose occurrence is suspected in classical novae.The 22Mg(p,γ)23Al reaction is relevant to ...The radionuclide 22Na generates the emission of a characteristic 1.275 MeVγ-ray.This is a potential astronomical observable,whose occurrence is suspected in classical novae.The 22Mg(p,γ)23Al reaction is relevant to the nucleosynthesis of 22Na in Ne-rich novae.In this study,employing the adiabatic distorted wave approximation and continuum discretized coupled channel methods,the squared neutron asymptotic normalization coefficients(ANCs)231 for the virtual decay of Ne→22Ne+n were extracted,and determined as(0.483±0.060)fm-1 and(9.7±2.3)fm-1 for the ground state and the first excited state from the experimental angular distributions of 22Ne(d,p)23Ne populating the ground state and the first excited state of 23Ne,respectively.Then,the squared proton ANC of 23Alg.s.was obtained as Cd5/22(23Al)(2.65±0.33)×103 fm-1 according to the charge symmetry of the strong interaction.The astrophysical S-factors and reaction rates for the direct capture contribution in 22Mg(p,γ)23Al were also presented.Furthermore,the proton width of the first excited state of 23Al was derived to be(57±14)eV from the neutron ANC of its mirror state in 23Ne and used to compute the contribution from the first resonance of 23Al.This result demonstrates that the direct capture dominates the 22Mg(p,γ)23Al reaction at most temperatures of astrophysical relevance for 0.33<T9<0.64.展开更多
The asymptotic normalization coefficients(ANCs) of the virtual decay ^(16)N→ ^(15)N + n are extracted from the ^(15)N(~7Li,~6Li)^(16)N reaction populating the ground and first three excited states in ^(16)N.The root-...The asymptotic normalization coefficients(ANCs) of the virtual decay ^(16)N→ ^(15)N + n are extracted from the ^(15)N(~7Li,~6Li)^(16)N reaction populating the ground and first three excited states in ^(16)N.The root-mean-square(rms) radii of the valence neutron in these four low-lying ^(16)N states are then derived by using the ANCs.The probabilities of the valence neutron staying out of the core potentials are found to be 31%± 8%,58%± 12%,32%±8%,and 60%± 12%.The present results support the conclusion that a one-neutron halo may be formed in the ^(16)N first and third excited states,while the ground and second excited states do not have a one-neutron halo structure.However,the core excitation effect has a strong influence on the one-neutron halo structure of the ground and first excited states in ^(16)N.展开更多
RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<su...RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.展开更多
This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin,et al.(2020).The authors replace the least squares estim...This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin,et al.(2020).The authors replace the least squares estimation in the first stage of Jin,et al.(2020)by M-estimation.The authors also provide the justification for not making any change in its second stage when the number of time periods is large enough.The proposed methodology is robust and efficient,and it can be easily implemented.In addition,the authors study the limiting behavior of the parameter estimators,which are shown to be consistent and asymptotic normally distributed under some conditions.Extensive simulation studies are carried out to assess the proposed procedure and a COVID-19 data example is conducted for illustration.展开更多
Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longit...Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.展开更多
In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute...In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute,an up-dating recursion procedure is proposed to simplify the com-putation of the estimators when a new observation is obtained.We show that,under mild conditions,the recursion estimates are strongly consistent.In addition,the asymptotic normality of the recursive constrained M-estimators of regression coeffcients is established.A Monte Carlo simulation study of the recursion estimates is also provided.Besides,robustness and asymptotic behavior of constrained M-estimators are briefly discussed.展开更多
Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension ...Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.展开更多
In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean s...In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean squared prediction error,and asymptotic normality of parameter vector are obtained.Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions.Finally,we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice.展开更多
In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random...In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.展开更多
By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove ...By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.展开更多
This paper investigates the hypothesis test of the parametric component in partial functional linear regression models.Based on a rank score function,the authors develop a rank test using functional principal componen...This paper investigates the hypothesis test of the parametric component in partial functional linear regression models.Based on a rank score function,the authors develop a rank test using functional principal component analysis,and establish the asymptotic properties of the resulting test under null and local alternative hypotheses.A simulation study shows that the proposed test procedure has good size and power with finite sample sizes.The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.展开更多
The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performan...The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.展开更多
A popular imputation method used to compensate for item nonresponse in sample surveys is thenearest neighbour imputation (NNI) method utilising a covariate to defined neighbours. Whenthe covariate is multivariate, how...A popular imputation method used to compensate for item nonresponse in sample surveys is thenearest neighbour imputation (NNI) method utilising a covariate to defined neighbours. Whenthe covariate is multivariate, however, NNI suffers the well-known curse of dimensionality andgives unstable results. As a remedy, we propose a single-index NNI when the conditional meanof response given covariates follows a single index model. For estimating the population meanor quantiles, we establish the consistency and asymptotic normality of the single-index NNI estimators. Some limited simulation results are presented to examine the finite-sample performanceof the proposed estimator of population mean.展开更多
In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes whic...In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years.So,the L_(2)-structure of the process is studied and its covariance function is given.These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process.Finite sample properties are also considered through Monte Carlo experiments.In end,the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar.展开更多
基金National Nature Science Foundation of China(No.60974030)the Chinese Universities Scientific Fund(No.CUSF-DH-D-2014059)
文摘The parameter estimation problem for an economic model called Constantinides-Ingersoll model is investigated based on discrete observations. Euler-Maruyama scheme and iterative method are applied to getting the joint conditional probability density function. The maximum likelihood technique is employed for obtaining the parameter estimators and the explicit expressions of the estimation error are given. The strong consistency properties of the estimators are proved by using the law of large numbers for martingales and the strong law of large numbers. The asymptotic normality of the estimation error for the diffusion parameter is obtained with the help of the strong law of large numbers and central-limit theorem. The simulation for the absolute error between estimators and true values is given and the hypothesis testing is made to verify the effectiveness of the estimators.
文摘In this article, the lifetime data subjecting to right random censoring is considered. Nonparametric estimation of the distribution function based on the conception of presmoothed estimation of relative-risk function and the properties of the estimator by using methods of numerical modeling are discussed. In the model under consideration, the estimates were compared using numerical methods to determine which of the estimates is actually better.
文摘Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.
基金supported by the National Natural Science Foundation of China under Grant Nos.12201079,12201004,and 11871072the National Social Science Foundation of China under Grant No.22BTJ059+1 种基金the Natural Science Foundation of Anhui Province under Grant Nos.2108085QA15 and 2108085MA06the“INSA Senior Scientist”scheme at the CR Rao Advanced Institute of Mathematics,Statistics and Computer Science,Hyderabad 500046,India.
文摘In this paper,the authors study a class of weighted version of probability density estimator.It is shown that the weighted estimator contains some existing estimators of probability density,no matter they are recursive or non-recursive.Some statistical results including weak consistency,strong consistency,rate of strong consistency,and asymptotic normality are established under some mild conditions.Moreover,the random weighted estimator is also investigated.Some numerical simulations and a real data analysis are presented to study the numerical performances of the estimators.
基金partially supported by the National Natural Science Foundation of China under Grant No.11801576the National Statistical Science Research Project of China under Grant No.2019LY59partially supported by the National Natural Science Foundation of China under Grant No.11871237。
文摘In the case of the differential privacy under the Laplace mechanism,the asymptotic properties of parameter estimators have been derived in some special network models with common binary values,but the asymptotic properties in network models with the ordered values are lacking.In this paper,the authors release the degree sequences of the ordered networks under a general noisy mechanism with the discrete Laplace mechanism as a special case.The authors establish the asymptotic result including the consistency and asymptotical normality of the parameter estimator when the number of parameters goes to infinity.Simulations and a real data example are provided to illustrate asymptotic results.
文摘This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.
基金Supported by the National Key Research and Development Program of China(2016YFA0400502)the National Natural Science Foundation of China(11975316,11490561,11535004,11775013)+1 种基金the Continuous Basic Scientific Research Project(WDJC-2019-13)the 973 Program(2013CB834406)。
文摘The radionuclide 22Na generates the emission of a characteristic 1.275 MeVγ-ray.This is a potential astronomical observable,whose occurrence is suspected in classical novae.The 22Mg(p,γ)23Al reaction is relevant to the nucleosynthesis of 22Na in Ne-rich novae.In this study,employing the adiabatic distorted wave approximation and continuum discretized coupled channel methods,the squared neutron asymptotic normalization coefficients(ANCs)231 for the virtual decay of Ne→22Ne+n were extracted,and determined as(0.483±0.060)fm-1 and(9.7±2.3)fm-1 for the ground state and the first excited state from the experimental angular distributions of 22Ne(d,p)23Ne populating the ground state and the first excited state of 23Ne,respectively.Then,the squared proton ANC of 23Alg.s.was obtained as Cd5/22(23Al)(2.65±0.33)×103 fm-1 according to the charge symmetry of the strong interaction.The astrophysical S-factors and reaction rates for the direct capture contribution in 22Mg(p,γ)23Al were also presented.Furthermore,the proton width of the first excited state of 23Al was derived to be(57±14)eV from the neutron ANC of its mirror state in 23Ne and used to compute the contribution from the first resonance of 23Al.This result demonstrates that the direct capture dominates the 22Mg(p,γ)23Al reaction at most temperatures of astrophysical relevance for 0.33<T9<0.64.
基金Supported by National Natural Science Foundation of China(11505117,11490560,11475264,11321064,11375269)Natural Science Foundation of Guangdong Province(2015A030310012)+1 种基金973 program of China(2013CB834406)National key Research and Development Province(2016YFA0400502)
文摘The asymptotic normalization coefficients(ANCs) of the virtual decay ^(16)N→ ^(15)N + n are extracted from the ^(15)N(~7Li,~6Li)^(16)N reaction populating the ground and first three excited states in ^(16)N.The root-mean-square(rms) radii of the valence neutron in these four low-lying ^(16)N states are then derived by using the ANCs.The probabilities of the valence neutron staying out of the core potentials are found to be 31%± 8%,58%± 12%,32%±8%,and 60%± 12%.The present results support the conclusion that a one-neutron halo may be formed in the ^(16)N first and third excited states,while the ground and second excited states do not have a one-neutron halo structure.However,the core excitation effect has a strong influence on the one-neutron halo structure of the ground and first excited states in ^(16)N.
文摘RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.
基金supported by the Natural Sciences and Engineering Research Council of Canada under Grant No.RGPIN-2017-05720the National Natural Science Foundation under Grant Nos.12201601,71873128,11571337,71631006,and 71921001the Anhui Provincial Natural Science Foundation under Grant No.2208085QA06。
文摘This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin,et al.(2020).The authors replace the least squares estimation in the first stage of Jin,et al.(2020)by M-estimation.The authors also provide the justification for not making any change in its second stage when the number of time periods is large enough.The proposed methodology is robust and efficient,and it can be easily implemented.In addition,the authors study the limiting behavior of the parameter estimators,which are shown to be consistent and asymptotic normally distributed under some conditions.Extensive simulation studies are carried out to assess the proposed procedure and a COVID-19 data example is conducted for illustration.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11922117,11771361)Fujian Provincial Science Fund for Distinguished Young Scholars(Grant No.2019J06004)。
文摘Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.
基金supported by the Natural Sciences and Engineering Research Council of Canada
文摘In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute,an up-dating recursion procedure is proposed to simplify the com-putation of the estimators when a new observation is obtained.We show that,under mild conditions,the recursion estimates are strongly consistent.In addition,the asymptotic normality of the recursive constrained M-estimators of regression coeffcients is established.A Monte Carlo simulation study of the recursion estimates is also provided.Besides,robustness and asymptotic behavior of constrained M-estimators are briefly discussed.
基金supported by the National Natural Science Foundation of China under Grant Nos.11871287,11501208,11771144,11801359the Natural Science Foundation of Tianjin under Grant No.18JCYBJC41100+1 种基金Fundamental Research Funds for the Central Universitiesthe Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin。
文摘Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671096,11690013,11731011 and 12071267)the Natural Science Foundation of Shanxi Province,China(Grant No.201901D111279)。
文摘In this paper,we consider composite quantile regression for partial functional linear regression model with polynomial spline approximation.Under some mild conditions,the convergence rates of the estimators and mean squared prediction error,and asymptotic normality of parameter vector are obtained.Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least-squares based method when there are outliers in the dataset or the random error follows heavy-tailed distributions.Finally,we apply the proposed methodology to a spectroscopic data sets to illustrate its usefulness in practice.
基金supported in part by the National Social Science Foundation of China(Grant No.20BTJ049).
文摘In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.
基金supported by the National Natural Science Foundation of China under Grant No.11601062the National Natural Science Foundation of China under Grant Nos.11971249+1 种基金partially supported by the National Natural Science Foundation of China under Grant Nos.11771330 and 11971203supported in part by the Fundamental Research Funds for the Central Universities under Grant Nos.11522110。
文摘By using Chen,Hou and Mu’s extended Zeilberger algorithm,the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials.Based on these recurrence relations,the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.
基金supported by the National Natural Science Foundation of China under Grant Nos.1177103211571340 and 11701020+1 种基金the Science and Technology Project of Beijing Municipal Education Commission under Grant Nos.KM201710005032 and KM201910005015the International Research Cooperation Seed Fund of Beijing University of Technology under Grant No.006000514118553。
文摘This paper investigates the hypothesis test of the parametric component in partial functional linear regression models.Based on a rank score function,the authors develop a rank test using functional principal component analysis,and establish the asymptotic properties of the resulting test under null and local alternative hypotheses.A simulation study shows that the proposed test procedure has good size and power with finite sample sizes.The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.
基金the China Postdoctoral Science Foundation under Grant No.2019M651422the National Natural Science Foundation of China under Grant Nos.71701127,11831008 and 11971171+3 种基金the National Social Science Foundation Key Program under Grant No.17ZDA091the 111 Project of China under Grant No.B14019the Natural Science Foundation of Shanghai under Grant Nos.17ZR1409000 and 20ZR1423000the Project of Humanities and Social Science Foundation of Ministry of Education under Grant No.20YJC910003。
文摘The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.
基金This work was partially supported by the National Natural Science Foundation of China grants 11831008 and 11871287the U.S.National Science Foundation grants DMS-1612873 and DMS-1914411the Natural Science Foundation of Tianjin(18JCYBJC41100)and the Fundamental Research Funds for the Central Universities.
文摘A popular imputation method used to compensate for item nonresponse in sample surveys is thenearest neighbour imputation (NNI) method utilising a covariate to defined neighbours. Whenthe covariate is multivariate, however, NNI suffers the well-known curse of dimensionality andgives unstable results. As a remedy, we propose a single-index NNI when the conditional meanof response given covariates follows a single index model. For estimating the population meanor quantiles, we establish the consistency and asymptotic normality of the single-index NNI estimators. Some limited simulation results are presented to examine the finite-sample performanceof the proposed estimator of population mean.
文摘In this paper,we study in frequency domain someprobabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion.This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years.So,the L_(2)-structure of the process is studied and its covariance function is given.These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process.Finite sample properties are also considered through Monte Carlo experiments.In end,the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar.
