Semiparametric partially linear varying coefficien

Authors: Xin He Xuenan Feng Xingwei Tong Xingqiu Zhao

Publish Date: 2016/04/27

Volume: 23, Issue: 3, Pages: 439-466

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Abstract

This paper studies semiparametric regression analysis of panel count data which arise naturally when recurrent events are considered Such data frequently occur in medical followup studies and reliability experiments for example To explore the nonlinear interactions between covariates we propose a class of partially linear models with possibly varying coefficients for the mean function of the counting processes with panel count data The functional coefficients are estimated by Bspline function approximations The estimation procedures are based on maximum pseudolikelihood and likelihood approaches and they are easy to implement The asymptotic properties of the resulting estimators are established and their finitesample performance is assessed by Monte Carlo simulation studies We also demonstrate the value of the proposed method by the analysis of a cancer data set where the new modeling approach provides more comprehensive information than the usual proportional mean modelThe authors would like to thank the Editor Professor MeiLing Ting Lee the Associate Editor and the two reviewers for their constructive and insightful comments and suggestions that greatly improved the paper Tong’s research was partly supported by BCMIIS NSF China Zhongdian Project 11131002 and NSFC No 10971015 Zhao’s research was partly supported by the Research Grants Council of Hong Kong PolyU 504011 and PolyU 503513 the Natural Science Foundation of China No 11371299 and The Hong Kong Polytechnic UniversityBy the similar arguments as those used in Wellner and Zhang 2007 again we can also show that hatLambda ps nt is uniformly bounded in probability for tin 0 b if mu 1b tau 0 for some 0btau or tin 0 tau if mu 1tau 0By HellySelection Theorem and compactness of Theta n it follows that hattheta nps=hatbeta ps n hatLambda ps n hatphi ps n has a subsequence hattheta ps n k=hatbeta ps n k hatLambda ps n k hatphi ps n k converging to theta +=beta + Lambda + phi + where Lambda + is a nondecreasing bound function on 0 b for 0btau and it can be defined on 0 tau if mu 1tau 0Spshatbeta ps nhatLambda ps nhatphi ps n Spsbeta 0Lambda 0 phi 0dotSpsbeta 0Lambda 0 phi 0hatbeta ps n beta 0hatLambda ps n Lambda 0 hatphi ps n phi 0=o pn1/2

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