This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in an additive fashion by an observed confounding variable. We propose a new identifiability condition by using the exponential calibration to obtain calibrated variables and propose a direct‐plug‐in estimator for the correlation coefficient. We show that the direct‐plug‐in estimator is asymptotically efficient. Next, we suggest an asymptotic normal approximation and an empirical likelihood‐based statistic to construct the confidence intervals. Last, 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 temperature forecast data set for an illustration.

中文翻译：

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相关系数的指数校准，具有加性失真测量误差

本文研究了未观察到的感兴趣变量之间的相关系数估计。这些无法观察到的变量会因观察到的混杂变量而以加法方式失真。通过使用指数校准来获得校准变量，我们提出了一种新的可识别性条件，并为相关系数提出了一种直接插入式估计器。我们证明了直接插入式估算器是渐近有效的。接下来，我们建议采用渐近正态近似和基于经验似然的统计量来构建置信区间。最后，我们提出了几种测试统计数据，以测试真实的相关系数是否为零。检验了所提出的检验统计量的渐近性质。我们进行了蒙特卡洛模拟实验，以检验所提出的估计量和检验统计量的性能。这些方法适用于分析温度预测数据集以进行说明。