Machine Learning Embedded Semiparametric Mixtures of Regressions with Covariate-Varying Mixing Proportions

• Published in: Econometrics and statistics Vol. 22; pp. 159 - 171
• Main Authors: Xue, Jiacheng, Yao, Weixin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2022
• Subjects: covariate-varying mixing proportions; neural network; Semiparametric mixture of regression; covariate-varying mixing proportions; Semiparametric mixture of regression; neural network
• ISSN: 2452-3062; 2452-3062
• DOI: 10.1016/j.ecosta.2021.10.018

A new class of semiparametric mixture regression models with covariate-varying mixing proportions is introduced by embedding machine learning methods into mixtures of regressions. The new method uses the neural network to estimate mixing proportions nonparametrically while using the maximum likelihood estimate to estimate all other component parameters. The new machine learning embedded semiparametric mixture regression models offer more flexible estimation compared to traditional parametric mixture regression models. More importantly, the new hybrid method could better estimate the effects of multivariate covariates nonparametrically than the traditional kernel regression methods, which suffer from the well known “curse of dimensionality”. The introduced hybrid idea can be easily extended to other semiparametric statistical models and other machine learning methods. Simulation studies and a real data application are used to demonstrate the effectiveness of the proposed new method and compare it with some other existing methods.