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Since its introduction, the skew-$t$ distribution has received much attentionin the literature both for the study of theoretical properties and as a modelfor data fitting in empirical work. A major motivation for this interest is thehigh degree of flexibility of the distribution as the parameters span theiradmissible range, with ample variation of the associated measures of skewnessand kurtosis. While this high flexibility allows to adapt a member of theparametric family to a wide range of data patterns, it also implies thatparameter estimation is a more delicate operation with respect to less flexibleparametric families, given that a small variation of the parameters can have asubstantial effect on the selected distribution. In this context, the aim ofthe present contribution is to deal with some computational aspects of maximumlikelihood estimation. A problem of interest is the possible presence ofmultiple local maxima of the log-likelihood function. Another one, to whichmost of our attention is dedicated, is the development of a quick and reliableinitialization method for the subsequent numerical maximization of thelog-likelihood function, both in the univariate and the multivariate context.

Some computational aspects of maximum likelihood estimation of the skew-$t$ distribution