Estimation of bivariate measurement error models with application to the corrupted Pearson correlation
Year: 2026
Type: article
Abstract: Measurement errors are common, yet most research focusses on a single error-prone covariate. In practice, multiple variables often exhibit correlated measurement errors. We propose a novel method for estimating a bivariate multiplicative measurement error model when both covariates are contaminated. Likelihood-based estimation in such models is computationally demanding due to repeated evaluation of two-dimensional integrals, especially for large samples. To address this, we exploit the lognormal error structure, which enables rewriting the likelihood integrals using cumulative distribution function values of the bivariate normal distribution. This significantly reduces computational cost and improves numerical stability. Simulation studies demonstrate the accuracy and efficiency of the proposed method. We further illustrate its practical utility by correcting a biased Pearson correlation and applying it to fetal biometry data.
Authors: Hohsuk Noh, Ingrid Van Keilegom
Institutions: Sookmyung Women's University, KU Leuven
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7153300896