TITLE:
On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence
AUTHORS:
Min Tsao
KEYWORDS:
Asymptotic Expansion; Asymptotic Normal Sequence; Edgeworth Expansion; Saddlepoint Expansion; Saddlepoints Expansion; Hermite Polynomials
JOURNAL NAME:
Open Journal of Statistics,
Vol.2 No.1,
January
6,
2012
ABSTRACT: 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.