Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models

• 成果类型: Article
• 署名作者: He, Heping; Severini, Thomas A.
• 署名单位: Northwestern University; University of Melbourne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000307
• 发表日期: 2007
• 页码: 2054-2074
• 关键词: edgeworth expansions; inference

摘要

Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order n(-1), where n is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as ((theta) over cap, a), where theta is the maximum likelihood estimator of the parameter theta of the model and a is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order n(-1) without making any assumption about the sufficient statistic of the model.