半参数线性混合效应模型的联合变量选择

发布时间：2018-06-27 04:48

本文选题：半参数线性混合效应模型 + 变量选择　；参考：《数理统计与管理》2017年03期

【摘要】：多数基于线性混合效应模型的变量选择方法分阶段对固定效应和随机效应进行选择,方法繁琐、易产生模型偏差,且大部分非参数和半参数的线性混合效应模型只涉及非参数部分的光滑度或者固定效应的选择,并未涉及非参变量或随机效应的选择。本文用B样条函数逼近非参数函数部分,从而把半参数线性混合效应模型转化为带逼近误差的线性混合效应模型。对随机效应的协方差矩阵采用改进的乔里斯基分解并重新参数化线性混合效应模型,接着对该模型的极大似然函数施加集群ALASSO惩罚和ALASSO惩罚两类惩罚,该法能实现非参数变量、固定效应和随机效应的联合变量选择,基于该法得出的估计量也满足相合性、稀疏性和Oracle性质。文章最后做了个数值模拟,模拟结果表明,本文提出的估计方法在变量选择的准确性、参数估计的精度两个方面均表现较好。
[Abstract]:Most variable selection methods based on linear mixed effect model are used to select fixed effect and random effect in stages. The method is cumbersome and easy to produce model deviation. And most of the nonparametric and semi-parametric linear mixed effect models only involve the choice of the smoothness or fixed effect of the non-parametric part, but not the non-parametric variable or the random effect. In this paper, B-spline function is used to approximate the nonparametric part of the function, thus the semi-parametric linear mixed effect model is transformed into the linear mixed effect model with approximation error. For the covariance matrix of random effects, the modified Giorinski decomposition and reparameterized linear mixed effect model are used, and then the cluster ALASSO penalty and ALASSO penalty are applied to the maximum likelihood function of the model, and the nonparametric variables can be realized by this method. The joint variable selection of fixed effect and random effect, the estimator based on this method also satisfies the consistency, sparsity and Oracle properties. Finally, a numerical simulation is done. The simulation results show that the proposed estimation method has good accuracy in variable selection and parameter estimation.
【作者单位】：暨南大学经济学院统计学系;
【基金】：国家社会科学基金重点项目(15ATJ001) 广东省委宣传部打造“理论粤军”2014年度重点课题(WT1407)的资助
【分类号】：O212

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