Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function

• 成果类型: Article
• 署名作者: Baraud, Y; Huet, S; Laurent, B
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); INRAE; Universite Paris Saclay; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000896
• 发表日期: 2005
• 页码: 214-257
• 关键词: Monotonicity

摘要

In this paper we propose a general methodology, based on multiple testing, for testing that the mean Of a Gaussian) vector in R(n) belongs to a convex set. We show that the test achieves its nominal level. and characterize a class of vectors over which the tests achieve a prescribed power, In the functional regression model this general methodology is applied to test some qualitative hypotheses oil the regression function. For example. we (est that the regression function is positive. increasing, convex, or more generally, satisfies a differential inequality. Uniform separation rates over classes of smooth functions are established and a comparison with other results in the literature is provided. A simulation study evaluates some of the procedures for testing monotonicity.