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

• 成果类型: Article
• 署名作者: Huang, Mian; Yao, Weixin
• 署名单位: Shanghai University of Finance & Economics; Kansas State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.682541
• 发表日期: 2012
• 页码: 711-724
• 关键词: bootstrap confidence bands; likelihood estimation; inferences

摘要

In this article, we study a class of semiparametric mixtures of regression models, in which the regression functions are linear functions of the predictors, but the mixing proportions are smoothing functions of a covariate. We propose a one-step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions. We derive the asymptotic bias and variance of the one-step estimate, and further establish its asymptotic normality. A modified expectation-maximization-type (EM-type) estimation procedure is investigated. We show that the modified EM algorithms preserve the asymptotic ascent property. Numerical simulations are conducted to examine the finite sample performance of the estimation procedures. The proposed methodology is further illustrated via an analysis of a real dataset.