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

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. (C) 2017 Elsevier B.V. All rights reserved.