Title: A new multivariate elliptical heavy-tailed distribution with application to allometry
Authors: Antonio Punzo - University of Catania (Italy) [presenting]
Luca Bagnato - Catholic University of the Sacred Heart (Italy)
Abstract: There are several real situations where the empirical distribution of multivariate real-valued data is elliptical and with heavy tails. Many statistical models already exist that accommodate these peculiarities. This branch of literature is enriched by introducing the multivariate shifted exponential normal (MSEN) distribution, an elliptical heavy-tailed generalization of the multivariate normal (MN). The MSEN belongs to the family of MN scale mixtures (MNSMs) by choosing a convenient shifted exponential as mixing distribution. The probability density function of the MSEN has a closed-form characterized by only one additional tailedness parameter, with respect to the nested MN, governing the tail weight. The first four moments exist, and the excess kurtosis can assume any positive value. The membership to the family of MNSMs simplifies maximum likelihood (ML) estimation of the parameters via the expectation-maximization (EM) algorithm; advantageously, the M-step is computationally simplified by closed-form updates of all the parameters. Since the tailedness parameter is estimated from the data, robust estimates of the mean vector of the nested MN distribution are automatically obtained by down weighting; we show this aspect theoretically but also by means of a simulation study. We fit the MSEN distribution to multivariate allometric data where we show its usefulness also in comparison with other well-established multivariate elliptical distributions.