线性混合效应模型的有效稳健经验似然推断

Efficient and Robust Empirical Likelihood Inferences for Linear Mixed Effects Models

本文考虑线性混合效应模型的有效稳健经验似然统计推断问题.通过结合众数回归方法和矩阵的QR分解技术,提出了一种基于众数回归的正交经验似然统计推断过程.证明提出的关于固定效应的经验对数似然比函数渐近服从中心卡方分布,进而构造了模型固定效应的置信区间.所提出的估计过程不需要对随机效应和模型误差的分布施加任何假定,并且关于固定效应的估计过程不受随机效应的影响,因此具有较好的稳健性和有效性.

This paper considers the efficient and robust empirical likelihood inference for linear mixed effects models.By combining modal regression method with QR decomposition technique,a modal regression based orthogonality empirical likelihood inference procedure is proposed.We further show that the proposed empirical log-likelihood ratio is asymptotically chi-squared,and then the confidence intervals for the fixed effects are constructed.The proposed estimation procedure does not need any assumption about the distributions of random effects and model errors,and the resulting estimators for fixed effects are not affected by the random effects.Hence,the proposed method is more robust and efficient.