Biometrika Advance Access originally published online on November 22, 2007
Biometrika 2007 94(4):921-937; doi:10.1093/biomet/asm066
Articles |
Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data
College of Applied Sciences, Beijing University of Technology, Beijing 100022, China lgxue{at}bjut.edu.cn
Department of Mathematics, Hong Kong Baptist University, Hong Kong, China lzhu{at}hkbu.edu.hk
Received for publication 1 November 2005. Revision received 1 March 2007.
A semiparametric regression model for longitudinal data is considered. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence regions and intervals. It is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made. Two calibrated empirical likelihood approaches to inference for the baseline function are developed. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence for the longitudinal semiparametric regression model, and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest. This leads us to prove a nonparametric version of Wilks' theorem. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation compares the empirical likelihood and normal-based methods in terms of coverage accuracies and average areas/lengths of confidence regions/intervals.
Key Words: Confidence region; Empirical likelihood • Longitudinal data • Maximum empirical likelihood estimator • Semiparametric regression model
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