Semiparametric statistical inferences for longitudinal data with nonparametric covariance modelling. Issue 6 (2nd November 2017)

• Record Type: Journal Article
• Authors: Xu, Qunfang; Bai, Yang
• Is Part Of: Statistics. Volume 51:Issue 6(2017)
• Page Start: 1280
• Page End: 1303
• Publication Date: 2017-11-02
• Subjects: Additive models -- nonparametric covariance modelling -- semiparametric regression -- splines approximation; 62H12 -- 62A01; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1354861
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: In this paper, semiparametric modelling for longitudinal data with an unstructured error process is considered. We propose a partially linear additive regression model for longitudinal data in which within-subject variances and covariances of the error process are described by unknown univariate and bivariate functions, respectively. We provide an estimating approach in which polynomial splines are used to approximate the additive nonparametric components and the within-subject variance and covariance functions are estimated nonparametrically. Both the asymptotic normality of the resulting parametric component estimators and optimal convergence rate of the resulting nonparametric component estimators are established. In addition, we develop a variable selection procedure to identify significant parametric and nonparametric components simultaneously. We show that the proposed SCAD penalty-based estimators of non-zero components have an oracle property. Some simulation studies are conducted to examine the finite-sample performance of the proposed estimation and variable selection procedures. A real data set is also analysed to demonstrate the usefulness of the proposed method.