Correcting the estimator for the mean vectors in a multivariate errors-in-variables regression model

TL;DR

This paper corrects the previously misderived estimators for mean vectors in multivariate errors-in-variables regression models, ensuring more accurate parameter estimation when both variables are measured with error.

Contribution

It provides the correct derivation of the estimators for the mean vectors, addressing errors in prior literature on multivariate errors-in-variables models.

Findings

Corrected estimators for mean vectors in the model

Clarification of previous derivation errors

Improved accuracy of parameter estimation

Abstract

The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional least squares approach to estimating the model parameters is biased and inconsistent. The generalized least squares, ordinary least squares and maximum likelihood estimators (under the assumption of Gaussian errors) were derived in the seminal paper of Gleser (1981). However, the ordinary least squares and maximum likelihood estimators for the mean vectors were incorrectly derived. In this short paper we amend this error, presenting the correct estimators of the mean vectors.