THE POWER AND OPTIMAL KERNEL OF THE BICKEL-ROSENBLATT TEST FOR GOODNESS OF FIT

• 成果类型: Article
• 署名作者: GHOSH, BK; HUANG, WM
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348133
• 发表日期: 1991
• 页码: 999-1009
• 关键词: density

摘要

Bickel and Rosenblatt proposed a procedure for testing the goodness of fit of a specified density to observed data. The test statistic is based on the distance between the kernel density estimate and the hypothesized density, and it depends on a kernel K, a bandwidth b(n) and an arbitrary weight function a. We study the behavior of the asymptotic power of the test and show that a uniform kernel maximizes the power when a > 0.