On the relationship between two asymptotic expansions for the distribution of sample mean and its applications

• 成果类型: Article
• 署名作者: Routledge, R; Tsao, M
• 署名单位: Simon Fraser University; University of Victoria
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 2200-2209
• 关键词: saddlepoint approximations

摘要

Although the cumulative distribution function may be differentiated to obtain the corresponding density function, whether or not a similar relationship exists between their asymptotic expansions remains a question. We provide a rigorous argument to prove that Lugannani and Rice's asymptotic expansion for the cumulative distribution function of the mean of a sample of i.i.d. observations may be differentiated to obtain Daniels's asymptotic expansion for the corresponding density function. We then apply this result to study the relationship between the truncated versions of the two series, which establishes the derivative of a truncated Lugannani and Rice series as an alternative asymptotic approximation for the density function. This alternative approximation in general does not need to be renormalized. Numerical examples demonstrating its accuracy are included.