Estimation of a convex function: Characterizations and asymptotic theory

• 成果类型: Article
• 署名作者: Groeneboom, P; Jongbloed, G; Wellner, JA
• 署名单位: Delft University of Technology; Vrije Universiteit Amsterdam; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1653-1698
• 关键词: regression

摘要

We study nonparametric estimation of convex regression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation case). We provide characterizations of these estimators, prove that they are consistent and establish their asymptotic distributions at a fixed point of positive curvature of the functions estimated. The asymptotic distribution theory relies on the existence of an invelope function for integrated two-sided Brownian motion +t(4) which is established in a companion paper by Groeneboom, Jongbloed and Wellner.