Improved estimation of the degree of freedom parameter of multivariate t-distribution

The multivariate t (MVT)-distribution is a widely used statistical model in various application domains, mainly due to its adaptability to heavy-tailed data. However, estimating the degree of freedom (d.o.f) parameter, that controls the shape of the distribution, remains a challenging problem. In this work, we develop a novel methodology and design various algorithms for estimating the d.o.f parameter. More precisely, based on a key relationship between scatter and covariance matrices for the t-distribution, the estimator is derived from the expectation of a particular quadratic form and is proved to converge although the classical independence assumption is not fulfilled. finally, some preliminary simulations show the improvement of the proposed approach with respect to state-of-the-art methods.