On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence

Min Tsao

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DOI: 10.4236/ojs.2012.21010                

Abstract

We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence X_n. 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 X_n. 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 X_n.

Keywords

Asymptotic Expansion; Asymptotic Normal Sequence; Edgeworth Expansion; Saddlepoint Expansion; Saddlepoints Expansion; Hermite Polynomials

Conflicts of Interest

The authors declare no conflicts of interest.

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