A penalized maximum likelihood approach for estimating mixture of regression models
Xianming Tan, Jianjun Xu, Zhang Runchu · Scientia Sinica Mathematica · 2019
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 estimatorfor mixture of regression models does not exist. We propose a penalized maximum likelihood approach for estimating the parameters ina mixture of regression models. We prove that the penalized maximum likelihood estimator (PMLE) is strongly consistent andasymptotically normal. Through extensive simulation studies, the proposed new estimator is shown to perform quitewell in terms of estimation accuracy. We also present a tone perception example to illustrate the applications of the theoretical results.