This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squar...This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.展开更多
Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asympt...Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.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
Partially linear varying coefficient model is a generalization of partially linear model and varying coefficient model and is frequently used in statistical modeling. In this paper, we construct estimators of the para...Partially linear varying coefficient model is a generalization of partially linear model and varying coefficient model and is frequently used in statistical modeling. In this paper, we construct estimators of the parametric and nonparametric components by Profile least-squares procedure which is based on local linear smoothing. The resulting estimators are shown to be asymptotically normal with heteroscedastic error.展开更多
Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coeffic...Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11771250the Natural Science Foundation of Shandong Province under Grant No.ZR2019MA002the Program for Scientific Research Innovation of Graduate Dissertation under Grant No.LWCXB201803
文摘This paper considers partially linear additive models with the number of parameters diverging when some linear cons train ts on the parame trie par t are available.This paper proposes a constrained profile least-squares estimation for the parametrie components with the nonparametric functions being estimated by basis function approximations.The consistency and asymptotic normality of the restricted estimator are given under some certain conditions.The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametrie components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypo theses.The finite sample performance of the proposed method is illus trated by simulation studies and a data analysis.
基金supported by National Natural Science Foundation of China (Grant No. 10871072)Natural Science Foundation of Shanxi Province of China (Grant No. 2007011014)PhD Program Scholarship Fund of ECNU 2009
文摘Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.
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the National Natural Science Foundation of China (No.10431010)
文摘Partially linear varying coefficient model is a generalization of partially linear model and varying coefficient model and is frequently used in statistical modeling. In this paper, we construct estimators of the parametric and nonparametric components by Profile least-squares procedure which is based on local linear smoothing. The resulting estimators are shown to be asymptotically normal with heteroscedastic error.
基金Supported by the National Natural Science Foundation of China(No.10571008)
文摘Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.
