Improved hypothesis testing in a general multivariate elliptical model

TL;DR

This paper develops improved hypothesis testing methods for a flexible multivariate elliptical regression model, enhancing finite sample performance over standard tests through adjusted likelihood ratio statistics.

Contribution

It introduces Skovgaard's and Barndorff-Nielsen's adjusted likelihood ratio tests for elliptical models, demonstrating their superior finite sample properties.

Findings

Proposed tests outperform standard tests in simulations.

Adjusted tests show better accuracy in finite samples.

Applications illustrate practical effectiveness of the methods.

Abstract

This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the error distribution. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal and Student-t distributions as special cases. We obtain Skovgaard's adjusted likelihood ratio statistics and Barndorff-Nielsen's adjusted signed likelihood ratio statistics and we conduct a simulation study. The simulations suggest that the proposed tests display superior finite sample behavior as compared to the standard tests. Two applications are presented in order to illustrate the methods.