Variable selection in robust semiparametric modeling for longitudinal data

• Published in: Journal of the Korean Statistical Society Vol. 43; no. 2; pp. 303 - 314
• Main Authors: Wang, Kangning, Lin, Lu
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.06.2014; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Longitudinal data; M-type estimator; Oracle property; Robustness; Semiparametric model; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Variable selection; 통계학; secondary; Oracle property; Robustness; Longitudinal data; Semiparametric model; M-type estimator; primary; Variable selection; primary 62G05 secondary 62E20
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2013.10.003

This paper considers robust variable selection in semiparametric modeling for longitudinal data with an unspecified dependence structure. First, by basis spline approximation and using a general formulation to treat mean, median, quantile and robust mean regressions in one setting, we propose a weighted M-type regression estimator, which achieves robustness against outliers in both the response and covariates directions, and can accommodate heterogeneity, and the asymptotic properties are also established. Furthermore, a penalized weighted M-type estimator is proposed, which can do estimation and select relevant nonparametric and parametric components simultaneously, and robustly. Without any specification of error distribution and intra-subject dependence structure, the variable selection method works beautifully, including consistency in variable selection and oracle property in estimation. Simulation studies also confirm our method and theories.