Improved estimation in a general multivariate elliptical model

TL;DR

This paper develops methods to reduce bias in maximum likelihood estimators within a flexible multivariate elliptical regression framework, applicable to various complex models, with demonstrated effectiveness through simulations.

Contribution

It derives second-order bias corrections and reductions for MLEs in a broad elliptical model, enhancing estimation accuracy in diverse statistical models.

Findings

Bias correction improves estimator accuracy

Bias reduction schemes are effective in simulations

Applicable to errors-in-variables, nonlinear mixed-effects, and heteroscedastic models

Abstract

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in common. Many frequently used models are special cases of this general formulation, namely: errors-in-variables models, nonlinear mixed-effects models, heteroscedastic nonlinear models, among others. In any of these models, the vector of the errors may have any multivariate elliptical distribution. We obtain the second-order bias of the maximum likelihood estimator, a bias-corrected estimator, and a bias-reduced estimator. Simulation results indicate the effectiveness of the bias correction and bias reduction schemes.