Testing uniformity versus a monotone density

• 成果类型: Article
• 署名作者: Woodroofe, M; Sun, JY
• 署名单位: University of Michigan System; University of Michigan; University System of Ohio; Case Western Reserve University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 338-360
• 关键词: poisson-process; intensity

摘要

The paper is concerned with testing uniformity versus a monotone density. This problem arises in two important contexts, after transformations, testing whether a sample is a simple random sample or a biased sample, and testing whether the intensity function of a nonhomogeneous Poisson process is constant against monotone alternatives. A penalized likelihood ratio test (P-test) and a Dip likelihood test (D-test) are developed. The D-test is analogous to Hartigan and Hartigan's (1985) Pip test for bump hunting problems. While nonparametric, both the P- and D-tests are quite efficient in comparison to the most powerful (NIP) tests for some simple alternatives and also the Laplace test developed for nonhomogeneous Poisson process. The P- and D-tests have higher power than the above MP tests under different sets of monotone alternatives and so have greater applicability. Moderate sample Size performance and applications of our tests are illustrated via simulations and examination of an air-conditioning equipment data set.