A conditional saddlepoint approximation for testing problems

• 成果类型: Article
• 署名作者: Gatto, R; Jammalamadaka, SR
• 署名单位: ESSEC Business School; University of California System; University of California Santa Barbara
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2670174
• 发表日期: 1999
• 页码: 533-541
• 关键词: small-sample asymptotics; distributions; probabilities; expansions; densities; variables

摘要

A saddlepoint approximation is provided for the distribution function of one M statistic conditional on another M statistic. Many interesting statistics based on dependent quantities (e.g., spacings, multinomial frequencies, rank differences) can be expressed in terms of independent identically distributed random variables conditioned on their sum, so that this conditional saddlepoint approximation yields accurate approximations for the distribution of such statistics. This saddlepoint approximation can also be used in conditional testing, where nuisance parameters are eliminated by conditioning on sufficient statistics.