Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data

A semiparametric regression model for longitudinal data is considered.The empirical likelihood method is used to estimate the regressioncoefficients and the baseline function, and to construct confidenceregions and intervals. It is proved that the maximum empiricallikelihood estimator of the regression coefficients achievesasymptotic efficiency and the estimator of the baseline functionattains asymptotic normality when a bias correction is made.Two calibrated empirical likelihood approaches to inferencefor the baseline function are developed. We propose a groupwiseempirical likelihood procedure to handle the inter-series dependencefor the longitudinal semiparametric regression model, and employbias correction to construct the empirical likelihood ratiofunctions for the parameters of interest. This leads us to provea nonparametric version of Wilks' theorem. Compared with methodsbased on normal approximations, the empirical likelihood doesnot require consistent estimators for the asymptotic varianceand bias. A simulation compares the empirical likelihood andnormal-based methods in terms of coverage accuracies and averageareas/lengths of confidence regions/intervals.