Likelihood ratio tests for monotone functions

• 成果类型: Article
• 署名作者: Banerjee, M; Wellner, JA
• 署名单位: University of Michigan System; University of Michigan; 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: 1699-1731
• 关键词: density

摘要

We study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data) and its limiting distribution is obtained. The limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving Brownian motion + l(2) and greatest convex minorants thereof. Inversion of the family of tests yields pointwise confidence intervals for the unknown distribution function. We also study the behavior of the statistic under local and fixed alternatives.