Asymptotics and the theory of inference

• 成果类型: Article; Proceedings Paper
• 署名作者: Reid, N
• 署名单位: University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1074290325
• 发表日期: 2003
• 页码: 1695-1731
• 关键词: higher-order asymptotics; approximate conditional inference; p-regression parameters; saddlepoint approximations; tail probabilities; accurate approximations; Edgeworth Expansion; confidence points; M-ESTIMATORS; likelihood

摘要

Asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable. More importantly, asymptotic analysis can also provide insight into the inference process itself, suggesting what information is available and how this information may be extracted. The development of likelihood inference over the past twenty-some years provides an illustration of the interplay between techniques of approximation and statistical theory.