Adjusted likelihood inference in an elliptical multivariate errors-in-variables model

TL;DR

This paper develops an adjusted likelihood ratio test for multivariate errors-in-variables models with elliptical error distributions, improving finite sample accuracy over standard tests.

Contribution

It introduces a modified likelihood ratio statistic for elliptical distributions, extending previous work to vector-valued parameters in multivariate errors-in-variables models.

Findings

The adjusted test follows a chi-squared distribution with high accuracy.

Simulation results show superior finite sample performance.

The method generalizes previous models to elliptical error distributions.

Abstract

In this paper we obtain an adjusted version of the likelihood ratio test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as a special case. We derive a modified likelihood ratio statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari(Advances in Statistical Analysis, 2010, 94, 75-87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard likelihood ratio test.