A NEW APPROACH TO TESTS AND CONFIDENCE BANDS FOR DISTRIBUTION FUNCTIONS

• 成果类型: Article
• 署名作者: Dumbgen, Lutz; Wellner, Jon A.
• 署名单位: University of Bern
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2249
• 发表日期: 2023
• 页码: 260-289
• 关键词: empirical distribution function; of-fit tests; asymptotic-distribution; HIGHER CRITICISM; inference

摘要

We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multiscale methods of testing and based on refined laws of the iterated logarithm for the normalized uniform empirical process U-n(t)/root t (1 - t) and its natural limiting process, the normalized Brownian bridge process U(t)/root t (1 - t). The new tests and confidence bands refine the procedures of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high power and accuracy of the latter meth-ods in the tail regions of distributions are essentially preserved while gaining considerably in the central region. The goodness-of-fit tests perform well in signal detection problems involving sparsity, as in Ingster (1997), Donoho and Jin (2004) and Jager and Wellner (2007), but also under contiguous alter-natives. Our analysis of the confidence bands sheds new light on the influence of the underlying phi-divergences.