On the Kendall Correlation Coefficient

TL;DR

This paper explores the properties of the Kendall rank correlation coefficient, deriving its expected value, proving its convergence, and proposing it as an alternative to Pearson's correlation, supported by illustrative examples.

Contribution

It introduces the expected value of the Kendall rank correlation as a new theoretical measure and analyzes its convergence properties.

Findings

Expected value of Kendall coefficient is independent of sample size

Kendall coefficient converges in probability to its expected value

Proposed Kendall-based measure as an alternative to Pearson correlation

Abstract

In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall rank correlation coefficient and show that the later is free of n. We also prove that in continuous case the Kendall correlation coefficient converges in probability to its expected value. We then propose to consider the expected value of the Kendall rank correlation coefficient as a new theoretical correlation coefficient which can be an alternative to the classical Pearson product-moment correlation coefficient. At the end of this work we analyze illustrative examples.