Mixture of Regression Models with Varying Mixing Proportions: A Semiparametric Approach

• Activity Number: 459
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Mian Huang*+ and Yao Weixin
• Companies: Shanghai University of Finance and Economics and Kansas State University
• Keywords: mixture model ; semiparametric modeling ; EM algorithm

Abstract

Motivated by an analysis of an CO2-GDP dataset, we propose a semiparametric mixture of regression models, in which the regression function is a linear function of the predictor but the mixing proportion is a smoothing function of the predictor. Compared to the Finite mixture of linear regression models, the newly proposed model is more flexible and data-driven. We study the model from likelihood point of view, and propose a one-step backfitting procedure for model estimation using EM algorithm and kernel regression. We derive the asymptotic bias and variance of the estimate, and further establish its asymptotic normality. To validate the proposed model, we propose a semiparametric likelihood ratio test to exam whether the proportion are a constant. Numerical simulations and real data analysis are presented.