Efficient inference about the tail weight in multivariate Student tt distributions

• We build a simple yet optimal test for the tail-weight of Student tt distributions.
• The tests are asymptotically equivalent to the Likelihood ratio test, but simpler.
• We can calculate the power of our tests.
• A Monte Carlo simulation study shows a good finite-sample behavior of the new tests.
• A financial data set is analyzed in detail via our new tests.

We propose a new testing procedure about the tail weight parameter of multivariate Student tt 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-nn 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.