Efficient Inference Based on Block Empirical Likelihood for Longitudinal Partially Linear Regression Models

Longitudinal data arises when subjects are followed over a period time. In this paper, we applied block empirical likelihood in partially linear regression model accounting for the within-subject correlation. For any working covariance matrix, an empirical log-likelihood ratio for the parametric components, which are of primary interest, is proposed, and the nonparametric version of the Wilk's theorem is derived. Simulations show that performance can be substantially improved by correctly specifying the correlation structure. At last, we illustrate the proposed method by analyzing an example in epidemiology.