ABSTRACT 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.

中文翻译：

---

相关系数的区间估计

摘要 相关系数 (CC) 是两个连续随机变量之间可能的线性关联的标准度量。CC 在许多科学学科中发挥着重要作用。对于二元正态分布，CC 有多种类型的置信区间，例如 z 变换和基于最大似然的区间。然而，当潜在的双变量分布未知时，CC 的置信区间的构建并不完善。在本文中，我们讨论了 CC 的各种区间估计方法。当基础双变量分布是正态分布时，我们为 CC 提出了一个广义置信区间，当基础双变量分布未知时，我们为 CC 提出了两个基于经验似然的区间。我们还进行了广泛的模拟研究，以在覆盖概率和区间长度方面比较新区间与现有区间。最后，通过两个真实的例子来演示所提出方法的应用。