On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence

• 作者: Min Tsao
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: ASYMPTOTIC EXPANSION ASYMPTOTIC NORMAL SEQUENCE Edgeworth EXPANSION Saddlepoint EXPANSION Saddlepoints EXPANSION HERMITE POLYNOMIALS
• 年，卷（期）: 2012,（1）
• 页码范围: 98-105
• 页数: 8页
• 分类号: O1

摘要

We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of Xn. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of Xn.