Bias correction in a multivariate normal regression model with general parameterization

TL;DR

This paper introduces a bias correction method for multivariate normal regression models with shared parameters in mean and covariance, applicable to various models including heteroscedastic and errors-in-variables, improving estimator accuracy.

Contribution

It provides a general second-order bias correction formula for maximum likelihood estimates in models with shared parameters, applicable to a wide range of regression models.

Findings

Bias correction yields nearly unbiased estimators in simulations.

The method is applicable to heteroscedastic and errors-in-variables models.

Empirical illustration demonstrates practical effectiveness.

Abstract

This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models available in the literature as special cases, such as (non)linear regression, errors-in-variables models, and so forth. Moreover, heteroscedastic situations may also be studied within our framework. We derive a general expression for the second-order biases of maximum likelihood estimates of the model parameters and show that it is always possible to obtain the second order bias by means of ordinary weighted lest-squares regressions. We enlighten such general expression with an errors-in-variables model and also conduct some simulations in order to verify the performance of the corrected estimates. The simulation results show that the bias correction scheme yields nearly unbiased estimators. We also present an empirical ilustration.