Efficient inference about the tail weight in multivariate Student $t$ distributions

TL;DR

This paper introduces a flexible, efficient testing procedure for the tail weight parameter in multivariate Student t-distributions, avoiding complex MLE and suitable for practical applications like finance.

Contribution

A new testing method based on Le Cam's approach that is as efficient as likelihood ratio tests but more flexible and easier to implement.

Findings

Test performs well in finite samples according to simulations.

Method successfully applied to financial data analysis.

Framework can be extended for efficient point estimation.

Abstract

We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root-$n$ consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.