A note on the permutation distribution of generalized correlation coefficients

TL;DR

This paper establishes conditions under which the generalized correlation coefficient's permutation distribution converges to a normal distribution, aiding statistical inference in symmetric data scenarios.

Contribution

It provides sufficient conditions for the asymptotic normality of generalized correlation coefficients under permutation null hypotheses.

Findings

Asymptotic normality holds under specified symmetry conditions.

Conditions applicable to a wide class of symmetric data matrices.

Facilitates hypothesis testing using permutation methods.

Abstract

We provide sufficient conditions for the asymptotic normality of the generalized correlation coefficient $\sum a_{ij}b_{ij}$ under the permutation null distribution when $a_{ij}$'s are symmetric and $b_{ij}$'s are symmetric.