Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters  

作　　者：WANG Xiuli ZHAO Shengli WANG Mingqiu 

机构地区：[1]School of Statistics, Qufu Normal University

出　　处：《Journal of Systems Science & Complexity》2019年第6期1747-1766,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.11771250;the Natural Science Foundation of Shandong Province under Grant No.ZR2019MA002;the Program for Scientific Research Innovation of Graduate Dissertation under Grant No.LWCXB201803

摘　　要：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.This paper considers partially linear additive models with the number of parameters diverging when some linear constraints on the parametric part are available. This paper proposes a constrained profile least-squares estimation for the parametric 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 parametric components,and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. The finite sample performance of the proposed method is illustrated by simulation studies and a data analysis.

关 键 词：B-spline basis constrained profile least-squares estimation diverging partially linear additive models profile likelihood ratio 

分 类 号：O17[理学—数学]