This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） prop...This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.展开更多
In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null d...In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.展开更多
In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero c...In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.展开更多
In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing respo...In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some sp...The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.展开更多
Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and...Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.展开更多
The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic ...The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.展开更多
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalizatio...This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.展开更多
This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,...This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.展开更多
This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear ...This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.展开更多
This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary...This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.展开更多
The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the l...The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.展开更多
In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least ...In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.展开更多
This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is...This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.展开更多
基金supported by the National Natural Science Funds for Distinguished Young Scholar (70825004)National Natural Science Foundation of China (NSFC) (10731010 and 10628104)+3 种基金the National Basic Research Program (2007CB814902)Creative Research Groups of China (10721101)Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics211 Project for Shanghai University of Financeand Economics (the 3rd phase)
文摘This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
文摘In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.
文摘In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.
基金Supported by National Natural Science Foundation of China （Grant No. 10871013）, Natural Science Foundation of Beijing （Grant No. 1072004）, and Natural Science Foundation of Guangxi Province （Grant No. 2010GXNSFB013051）
文摘In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
基金supported by National Natural Science Foundation of China (Grant Nos. 11401006, 11671299 and 11671042)a grant from the University Grants Council of Hong Kong+1 种基金the China Postdoctoral Science Foundation (Grant No. 2017M611083)the National Statistical Science Research Program of China (Grant No. 2015LY55)
文摘The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.
基金Supported by the National Natural Science Foundation of China (No. 10871177)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20090101110020)
文摘Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components： model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609+1 种基金the Doctor's Start-up Research Fund under Grant No. 08-52204the Youth Science Research Fund of Chongging Technology and Business University under Grant No. 0852008
文摘The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.
基金Supported by the National Natural Science Foundation of China(No.10771017,No.10231030)Key Project of Ministry of Education,PRC(No.309007)
文摘This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.
基金Supported by the National Natural Science Foundation of China (No.40574003) the National Natural Science of Hunan (NO.03JJY3065).
文摘This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X^Tβ ＋Z^Tα（T） ＋ε,ξ = X ＋ η with the identifying condition E[（ε,η^T）^T] =0, Cov[（ε,η^T）^T] = σ^2Ip＋1. The estimators of interested regression parameters /3 , and the model error variance σ2, as well as the nonparametric components α（T）, are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ2 are strongly consistent and asymptotically normal and that the estimator of α（T） achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the VN,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.
基金supported by Natural Natural Science Foundation of China (Grant Nos.10771017,10901020)Key Project of Chinese Ministry of Education (Grant No.309007)
文摘This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method.
基金Supported by National Natural Science Foundation of China (Grant Nos.10771017,10971015,10901020)Key Project of MOE,PRC (Grant No.309007)
文摘This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.
基金supported in part by National Natural Science Foundation of China(11171112,11201190)Doctoral Fund of Ministry of Education of China(20130076110004)+1 种基金Program of Shanghai Subject Chief Scientist(14XD1401600)the 111 Project of China(B14019)
文摘The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al. （2008） proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized like- lihood ratio test is established. Under the null hypotheses the normalized test statistic follows a x2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance param- eters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.
基金Supported by the Educational Commission of Hubei Province of China(Grant No.D20112503)National Natural Science Foundation of China(Grant Nos.11071022,11231010 and 11028103)the foundation of Beijing Center of Mathematics and Information Sciences
文摘In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.
文摘This paper simultaneously investigates variable selection and imputation estimation of semiparametric partially linear varying-coefficient model in that case where there exist missing responses for cluster data. As is well known, commonly used approach to deal with missing data is complete-case data. Combined the idea of complete-case data with a discussion of shrinkage estimation is made on different cluster. In order to avoid the biased results as well as improve the estimation efficiency, this article introduces Group Least Absolute Shrinkage and Selection Operator (Group Lasso) to semiparametric model. That is to say, the method combines the approach of local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator. In that case, it can conduct nonparametric estimation and variable selection in a computationally efficient manner. According to the same criterion, the parametric estimators are also obtained. Additionally, for each cluster, the nonparametric and parametric estimators are derived, and then compute the weighted average per cluster as finally estimators. Moreover, the large sample properties of estimators are also derived respectively.
