BOUNDS FOR THE ASYMPTOTIC DISTRIBUTION OF THE LIKELIHOOD RATIO

• 成果类型: Article
• 署名作者: Anastasiou, Andreas; Reinert, Gesine
• 署名单位: University of Cyprus; University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1510
• 发表日期: 2020
• 页码: 608-643
• 关键词: normal approximation; tests

摘要

In this paper, we give an explicit bound on the distance to chi-square for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge, this is the first explicit bound which is available in the literature. The bound depends on the number of samples as well as on the dimension of the parameter space. We illustrate the bound with three examples: samples from an exponential distribution, samples from a normal distribution and logistic regression.