Fisher transformation via Edgeworth expansion
Statistics Theory
2022-08-11 v1 Statistics Theory
Abstract
We show how to calculate individual terms of the Edgeworth series to approximate the distribution of the Pearson correlation coefficient with the help of a simple Mathematica program. We also demonstrate how to eliminate the corresponding skewness, thus making the approximation substantially more accurate. This leads, in a rather natural way, to deriving a superior (in terms of its accuracy) version of Fisher's z transformation. The code can be easily modified to deal with any sample statistics defined as a function of several sample means, based on a random independent sample from a multivariate distribution.
Keywords
Cite
@article{arxiv.2208.05070,
title = {Fisher transformation via Edgeworth expansion},
author = {Jan Vrbik},
journal= {arXiv preprint arXiv:2208.05070},
year = {2022}
}