Comparing Seventeen Interval Estimates for a Bivariate Normal Correlation Coefficient

TL;DR

This paper compares seventeen methods for constructing confidence intervals for the correlation coefficient in bivariate normal distributions, evaluating their coverage, length, and robustness through simulations and real data examples.

Contribution

It introduces a generalized and a bootstrap confidence interval, and provides a comprehensive comparison of seventeen approaches.

Findings

Several methods achieve accurate coverage probabilities.

The proposed generalized and bootstrap intervals perform well in robustness tests.

Different approaches vary in expected length and robustness depending on distribution assumptions.

Abstract

In this paper, we consider the problem of constructing confidence interval for the correlation coefficient in a bivariate normal distribution. For this problem, we found fifteen approaches in literatures. Also, we have proposed a generalized confidence interval and a parametric bootstrap confidence interval. The coverage probabilities and expected lengths of these seventeen approaches are evaluated and compared via simulation study. In addition, robustness of the methods is considered in the comparisons by the non-normal distributions. Two real examples are given to illustrate the approaches.