NONPARAMETRIC LEAST SQUARES ESTIMATION OF A MULTIVARIATE CONVEX REGRESSION FUNCTION

• 成果类型: Article
• 署名作者: Seijo, Emilio; Sen, Bodhisattva
• 署名单位: Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS852
• 发表日期: 2011
• 页码: 1633-1657
• 关键词: maximum-likelihood-estimation; log-concave density; Consistency; monotone

摘要

This paper deals with the consistency of the nonparametric least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided.