Edgeworth expansion and normalizing transformation of ratio statistics and their application

Yoshihiko Maesono

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Some statistics in common use take the form of a ratio of two statistics, such as sample correlation coefficient, Pearson's coefficient of variation, cumulant estimators, and so on. In this article, using an asymptotic representation of the ratio statistics, we will obtain an Edgeworth expansion and a normalizing transformation with remainder term o(n-1/2). The Edgeworth expansion is based on a Studentized ratio statistic, which is studentized by a consistent variance estimator. Applying these results to the sample correlation coefficient, we obtain the normalizing transformation and an asymptotic confidence interval of the correlation coefficient without assuming specific underlying distribution. This normalizing transformation is an extension of the Fisher's z-transformation.

Original languageEnglish
Pages (from-to)1344-1358
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Volume39
Issue number8-9
DOIs
Publication statusPublished - Jan 1 2010

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Normalizing Transformation
Edgeworth Expansion
Correlation coefficient
Statistics
Product-moment correlation
Asymptotic Representation
Variance Estimator
Coefficient of variation
Consistent Estimator
Cumulants
Error term
Statistic
Confidence interval
Estimator

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Edgeworth expansion and normalizing transformation of ratio statistics and their application. / Maesono, Yoshihiko.

In: Communications in Statistics - Theory and Methods, Vol. 39, No. 8-9, 01.01.2010, p. 1344-1358.

Research output: Contribution to journalArticle

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