一种惩罚最大似然方法估计混合回归模型  

A penalized maximum likelihood approach for estimating mixture of regression models

作　　者：徐建军 谭鲜明 张润楚[3] Jianjun Xu;Xianming Tan;Runchu Zhang

机构地区：[1]浙江财经大学金融学院,杭州310018 [2]The Methodology Center, The Pennsylvania State University, University Park, PA 16802, USA [3]南开大学数学学院,天津300071

出　　处：《中国科学：数学》2019年第8期1159-1182,共24页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:71631005);教育部人文社科(批准号:12YJC910011);浙江省自然科学基金(批准号:LY18G010015);国家统计科学研究(批准号:2017LY74)资助项目

摘　　要：本文考虑具有正态误差假设下混合回归模型的参数估计问题.由于似然函数的无界性,混合回归模型普通的最大似然估计不存在.本文提出一种惩罚最大似然方法来估计混合回归模型的参数,证明惩罚最大似然估计量(penalized maximum likelihood estimation, PMLE)具有强相合和渐近正态性.通过深入模拟研究,从估计精确性角度看,惩罚最大似然估计量有很好的表现.本文还给出一个音调感知的例子来说明理论结果的应用.This paper considers the parameter estimation problem for mixture of regression models with normal errors. Because of unboundedness of the likelihood function, the ordinary maximum likelihood estimator for mixture of regression models does not exist. We propose a penalized maximum likelihood approach for estimating the parameters in a mixture of regression models. We prove that the penalized maximum likelihood estimator(PMLE) is strongly consistent and asymptotically normal. Through extensive simulation studies, the proposed new estimator is shown to perform quite well in terms of estimation accuracy. We also present a tone perception example to illustrate the applications of the theoretical results.

关 键 词：混合回归 惩罚最大似然估计量 强相合 渐近正态 

分 类 号：O212.1[理学—概率论与数理统计]