Efficient inference about the tail weight in multivariate Student t distributions

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. Keywords and Phrases: efficient testing procedures; likelihood ratio test; local asymptotic normality; Student t distribution; tail weight