Abstract In this article, two-stage and fixed sample size procedures are developed for constructing confidence intervals for the common correlation ρ of an equi-correlated multivariate normal distribution. Two different approaches for estimation are considered, namely, fixed-width and bounded-width interval estimation. In the fixed-width confidence interval estimation problem, a two-stage procedure is developed and the exact distribution of the corresponding stopping variable and the exact coverage probability of the interval estimator are derived. Asymptotic optimality properties such as asymptotic first-order efficiency and asymptotic consistency properties of the two-stage procedure are established. Bounded-width confidence intervals are obtained by applying fixed-accuracy estimation methodologies of Mukhopadhyay and Banerjee (2014, 2015a,b) and Banerjee and Mukhopadhyay (2016) using different transformations on ρ. Both fixed sample size and two-stage sampling methodologies for bounded-width confidence interval estimation of are developed incorporating such transformations. Finally, performances of all the procedures are compared via extensive sets of simulation studies.

中文翻译：

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等相关多元正态分布中公共相关的两阶段固定宽度和有界宽度置信区间估计方法

摘要 在本文中，开发了两阶段固定样本量程序，用于为等相关多元正态分布的公共相关性 ρ 构建置信区间。考虑了两种不同的估计方法，即固定宽度和有界宽度区间估计。在固定宽度置信区间估计问题中，开发了一个两阶段程序，并推导出相应停止变量的精确分布和区间估计器的精确覆盖概率。建立了两阶段过程的渐近最优特性，例如渐近一阶效率和渐近一致性特性。通过应用 Mukhopadhyay 和 Banerjee (2014, 2015a, b) 以及 Banerjee 和 Mukhopadhyay (2016) 在 ρ 上使用不同的变换。用于有界宽度置信区间估计的固定样本大小和两阶段抽样方法都是结合此类转换而开发的。最后，通过大量模拟研究比较所有程序的性能。