TESTING NONPARAMETRIC SHAPE RESTRICTIONS

• 成果类型: Article
• 署名作者: Komarova, Tatiana; Hidalgo, Javier
• 署名单位: University of Manchester; University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2311
• 发表日期: 2023
• 页码: 2299-2317
• 关键词: model checks; convex function; regression; MONOTONICITY; splines

摘要

We describe and examine a test for a general class of shape constraints, such as signs of derivatives, U-shape, quasi-convexity, log-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of a Brownian motion index by the c.d.f. of the regressor. As a result, the test is distribution-free and critical values are readily available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.