Interval Estimation for the Correlation Coefficient

The correlation coefficient (CC) is a standard measure of a possible linear association between two continuous random variables. The CC plays a significant role in many scientific disciplines. For a bivariate normal distribution, there are many types of confidence intervals for the CC, such as z-transformation and maximum likelihood-based intervals. However, when the underlying bivariate distribution is unknown, the construction of confidence intervals for the CC is not well-developed. In this paper, we discuss various interval estimation methods for the CC. We propose a generalized confidence interval for the CC when the underlying bivariate distribution is a normal distribution, and two empirical likelihood-based intervals for the CC when the underlying bivariate distribution is unknown. We also conduct extensive simulation studies to compare the new intervals with existing intervals in terms of coverage probability and interval length. Finally, two real examples are used to demonstrate the application of the proposed methods.