Orthogonality-based empirical likelihood inference for varying-coefficient partially nonlinear model with longitudinal data

Abstract

In this paper, we study empirical likelihood-based inference for longitudinal data with varying-coefficient partially nonlinear model. Based on the orthogonality estimation technology, the QR decomposition is firstly used to separate the nonparametric component in the model. With the quadratic inference functions (QIF), we propose an estimator for the parameter that avoids estimating the nuisance parameter in the correlation matrix directly. In addition, we construct an empirical log-likelihood ratio statistic for the parameter and obtain the maximum empirical likelihood (MEL) estimator. The proposed MEL estimator has the same asymptotic variance as the QIF estimator and is more efficient than the estimator from the conventional generalized estimating equations (GEE). Under some assumptions, we establish certain asymptotic properties of the resulting estimators. Furthermore, we conduct simulation studies to evaluate the performances of the proposed estimation procedures in finite samples.