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.

摘要

在本文中，我们研究了具有变系数部分非线性模型的纵向数据的基于经验似然的推理。基于正交性估计技术，首先采用QR分解分离模型中的非参数分量。使用二次推理函数（QIF），我们提出了一个参数估计器，避免了直接估计相关矩阵中的有害参数。此外，我们为参数构建了一个经验对数似然比统计量，并获得了最大经验似然 (MEL) 估计量。所提出的 MEL 估计器具有与 QIF 估计器相同的渐近方差，并且比来自传统广义估计方程 (GEE) 的估计器更有效。在一些假设下，我们建立了结果估计量的某些渐近性质。此外，我们进行了模拟研究，以评估所提出的估计程序在有限样本中的性能。