English

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}
}