New goodness-of-fit tests and their application to nonparametric confidence sets

• 成果类型: Article
• 署名作者: Dümbgen, L
• 署名单位: Ruprecht Karls University Heidelberg; University of Lubeck
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 288-314
• 关键词: asymptotic equivalence; white-noise; regression; densities

摘要

Suppose one observes a process V on the unit interval, where dV = f(o)+ dW with an unknown parameter f(o) epsilon L-1[0, 1] and standard Brownian motion W. We propose a particular test of one-point hypotheses about f(o) which is based on suitably standardized increments of V. This test is shown to have desirable consistency properties if, for instance, f(o) is restricted to various Holder classes of functions. The test is mimicked in the context of nonparametric density estimation, nonparametric regression and interval-censored data. Under shape restrictions on the parameter, such as monotonicity or convexity, we obtain confidence sets for f(o) adapting to its unknown smoothness.