Estimation of correlation coefficient under a linear multiplicative distortion measurement errors model

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a new multiplicative fashion by an observed confounding variable, namely, a parametric distortion measurement errors model. The least squares estimatio...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2024-01, Vol.53 (1), p.62-93
Main Authors: Zhang, Jun, Yang, Baojun, Feng, Zhenghui
Format: Article
Language:English
Subjects:
Asymptotic properties
Calibration
Confidence intervals
Correlation coefficient
Correlation coefficients
Distortion
Empirical analysis
Errors
Estimators
Least squares
Monte Carlo simulation
multiplicative measurement errors
Parameter estimation
parametric distortion
Statistical analysis
Variables
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Summary:This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a new multiplicative fashion by an observed confounding variable, namely, a parametric distortion measurement errors model. The least squares estimation and weighted least squares estimation are used to estimate parameters in the multiplicative distortion functions. An interesting finding is that the calibrated variables obtained by using the weighted least squares estimators perform asymptotic equivalent to the calibrated variables obtained from the nonparametric kernel smoothing estimators in the literature. We then used the calibrated variables to estimate the correlation coefficient, and show that the proposed estimators of correlation coefficient are all asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence intervals. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators. These methods are applied to analyze two real datasets for an illustration.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2021.2004421