Abstract

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a multiplicative fashion by an observed confounding variable. We propose a new identifiability condition by using the absolute logarithmic calibration to obtain calibrated variables and the direct-plug-in estimator for the correlation coefficient. We show that the direct-plug-in estimator is asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the 2 confidence intervals. Next, we propose several test statistics for testing whether the true correlation coefficient is zero or not. The asymptotic properties of the proposed test statistics are examined. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration.

摘要

本文研究了未观察到的感兴趣变量之间相关系数的估计。这些不可观察的变量被观察到的混杂变量以乘法方式扭曲。我们通过使用绝对对数校准来获得校准变量和相关系数的直接插入估计器来提出新的可识别性条件。我们表明直接插入式估计器是渐近有效的。此外，我们建议使用渐近正态近似和基于经验似然的统计来构建 2 个置信区间。接下来，我们提出了几个检验统计量来检验真实相关系数是否为零。检查了所提出的检验统计量的渐近特性。我们进行了蒙特卡罗模拟实验，以检查所提出的估计量和测试统计量的性能。这些方法用于分析真实数据集以进行说明。