Subject-wise empirical likelihood inference in partial linear models for longitudinal data

Abstract

In analyzing longitudinal data, within-subject correlations are a major factor that affects statistical efficiency. Working with a partially linear model for longitudinal data, a subject-wise empirical likelihood based method that takes the within-subject correlations into consideration is proposed to estimate the model parameters. A nonparametric version of the Wilks Theorem for the limiting distribution of the empirical likelihood ratio, which relies on a kernel regression smoothing method to properly centered data, is derived. The estimation of the nonparametric baseline function is also considered. A simulation study and an application are reported to investigate the finite sample properties of the proposed method. The numerical results demonstrate the usefulness of the proposed method.