A class of grouped Brunk estimators and penalized spline estimators for monotone regression

• 成果类型: Article
• 署名作者: Wang, Xiao; Shen, Jinglai
• 署名单位: Purdue University System; Purdue University; University System of Maryland; University of Maryland Baltimore County
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq029
• 发表日期: 2010
• 页码: 585601
• 关键词: smoothing splines; CONVERGENCE; convex; SUM

摘要

We study a class of monotone univariate regression estimators. We use B-splines to approximate an underlying regression function and estimate spline coefficients based on grouped data. We investigate asymptotic properties of two monotone estimators: a grouped Brunk estimator and a penalized monotone estimator. These estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression function. Asymptotic distributions are developed and are shown to be independent of spline degrees and the number of knots. Simulation results and car data illustrate performance of the proposed estimators.