The efficiency of the likelihood ratio to choose between a t-distribution and a normal distribution

TL;DR

This paper evaluates the effectiveness of the likelihood ratio test in distinguishing between t-distribution and normal distribution errors in regression and time series models, using entropy properties and simulations.

Contribution

It provides a theoretical and empirical analysis of the likelihood ratio's performance in selecting the correct error distribution.

Findings

Likelihood ratio effectively differentiates heavy-tailed from Gaussian errors.

Simulation results support the theoretical entropy-based analysis.

The method shows high probability of correct distribution choice in various scenarios.

Abstract

A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of the likelihood ratio to choose between the two distributions is investigated using entropy properties and a simulation study. The proportion of times or probability that the likelihood of the correct assumption will be bigger than the likelihood of the incorrect assumption is estimated.