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Empirical likelihood semiparametric regression analysis for longitudinal data

机译：纵向数据的经验似然半参数回归分析

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摘要

A semiparametric regression model for longitudinal data is considered. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence regions and intervals. It is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made. Two calibrated empirical likelihood approaches to inference for the baseline function are developed. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence for the longitudinal semiparametric regression model, and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest. This leads us to prove a nonparametric version of Wilks' theorem. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation compares the empirical likelihood and normal-based methods in terms of coverage accuracies and average areas/lengths of confidence regions/intervals.
机译：考虑纵向数据的半参数回归模型。经验似然法用于估计回归系数和基线函数，并构造置信区域和区间。证明了当进行偏差校正时，回归系数的最大经验似然估计值达到渐近效率，基线函数的估计值达到渐近正态性。开发了两种校准的经验似然方法来推断基线函数。我们提出了一种按组的经验似然程序来处理纵向半参数回归模型的系列间相关性，并采用偏差校正来构造感兴趣参数的经验似然比函数。这使我们证明了威尔克斯定理的非参数形式。与基于正态近似的方法相比，经验似然不需要渐近方差和偏差的一致估计量。模拟在覆盖率准确性和置信区域/区间的平均面积/长度方面比较了经验似然法和基于法线的方法。

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