Exploring the multiple correlation coefficient under multiplicative distortion measurement errors

Xiaodi Wang

doi:10.1080/02331888.2025.2601249

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Exploring the multiple correlation coefficient under multiplicative distortion measurement errors

2025-12-01

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Xiaodi Wang

Jun Zhang *

DOI：10.1080/02331888.2025.2601249

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Abstract

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The multiple correlation coefficient is a fundamental metric in multivariate statistical analysis, measuring the linear relationship between a dependent variable and multiple independent variables. This study delves into its application within multiplicative distortion measurement errors models, where an unobservable covariate vector is distorted by a multiplicative function involving a confounding variable. To address this, we introduce two conditional mean calibration methodologies to generate proxies for the unobservable vector. Initially focussing on triple-variable scenarios, we present asymptotic results for calibrated estimators and test statistics, then extend our analysis to p-dimensional vectors under both normal and general distributions. Theoretical findings highlight asymptotically efficient estimators and test statistics. Monte Carlo simulations empirically validate these results, and an analysis of a clinical dataset provides a practical illustration.

Keywords:

Calibration

kernel smoothing

multiplicative distortion

multiple correlation coefficient