Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

TL;DR

This paper introduces modified likelihood ratio tests for heteroskedastic errors-in-variables multivariate regression models with elliptical error distributions, improving finite sample performance and applicability in real-world data.

Contribution

It develops Skovgaard-adjusted likelihood ratio tests for heteroskedastic multivariate errors-in-variables models with elliptical errors, enhancing test accuracy.

Findings

Proposed tests outperform standard likelihood ratio tests in finite samples.

Adjusted tests follow chi-squared distribution with high accuracy.

Application to cardiovascular data demonstrates practical usefulness.

Abstract

In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behavior as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Projection cardiovascular disease.