标题： 线性混合效应模型中的变量选择 显示英文标题

标题： Variable selection in linear mixed effects models

摘要： 本文关注于线性混合效应模型中固定效应和随机效应的选择与估计。 我们提出了一类非凹惩罚轮廓似然方法，用于选择和估计重要的固定效应。 为了解决随机效应未知协方差矩阵的困难，我们建议在惩罚轮廓似然中使用一个代理矩阵。 我们建立了代理矩阵选择的条件，并证明所提出的程序具有模型选择一致性，允许固定效应的数量以指数速度增长与样本量有关。 我们进一步提出了一个组变量选择策略，以同时选择和估计重要的随机效应，在该策略中用代理矩阵代替了随机效应未知的协方差矩阵。 我们证明了，当代理矩阵被适当地选择时，所提出的程序可以以渐近概率为一识别所有真实的随机效应，其中随机效应向量的维度允许以指数速度增长与样本量有关。 通过蒙特卡罗模拟研究检验了所提出程序的有限样本性能。 我们进一步通过一个真实数据例子展示了所提出的方法。 显示英文摘要

摘要： This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size. We further propose a group variable selection strategy to simultaneously select and estimate important random effects, where the unknown covariance matrix of random effects is replaced with a proxy matrix. We prove that, with the proxy matrix appropriately chosen, the proposed procedure can identify all true random effects with asymptotic probability one, where the dimension of random effects vector is allowed to increase exponentially with the sample size. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. We further illustrate the proposed procedures via a real data example.