The Assessment of Performance of Correlation Estimates in Discrete Bivariate Distributions Using Bootstrap Methodology

TL;DR

This paper evaluates the performance of Pearson's and Spearman's correlation estimators for discrete bivariate distributions, using bootstrap and classical methods, with simulations showing Pearson's estimator is slightly more efficient.

Contribution

It compares Pearson's and Spearman's correlation estimators for discrete distributions using bootstrap confidence intervals and simulation, highlighting their relative efficiency and bias.

Findings

Pearson's estimator performs slightly better than Spearman's.

Bootstrap methods are effective for constructing confidence intervals.

Simulation results support the efficiency comparison.

Abstract

Little attention has been given to the correlation coefficient when data come from discrete or continuous non-normal populations. In this article, we consider the efficiency of two correlation coefficients which are from the same family, Pearson's and Spearman's estimators. Two discrete bivariate distributions were examined: the Poisson and the Negative Binomial. The comparison between these two estimators took place using classical and bootstrap techniques for the construction of confidence intervals. Thus, these techniques are also subject to comparison. Simulation studies were also used for the relative efficiency and bias of the two estimators. Pearson's estimator performed slightly better than Spearman's.