Estimation of correlation coefficient with general distortion measurement errors

This article studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in both multiplicative and additive fashion by an observed confounding variable. We propose several estimators for the correlation coefficient. Some of...

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Bibliographic Details
Published inCommunications in statistics. Simulation and computation Vol. 52; no. 9; pp. 4491 - 4521
Main Authors Zhang, Jun, Lin, Bingqing
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.09.2023
Taylor & Francis Ltd
Subjects
Additive distortion
Asymptotic properties
Calibration
Confidence intervals
Correlation coefficient
Correlation coefficients
Distortion
Empirical analysis
Estimators
Kernel smoothing
Monte Carlo simulation
Multiplicative distortion
Statistical analysis
Statistical methods
Statistical tests
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Summary:This article studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in both multiplicative and additive fashion by an observed confounding variable. We propose several estimators for the correlation coefficient. Some of estimators are shown to be asymptotically efficient as if there are no distortions in the variables. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence intervals. An improved estimation method for no additive distortion scenario is also considered. 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.
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ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2021.1963453