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Adelchi Azzalini, Padua U. Print
Friday, 28 September 2012, 14:30 - 15:30

Adelchi Azzalini, University of Padua

On the problem of ML estimates on the boundary of the parameter space for skew-normal and skew-$t$ distributions.

ABSTRACT: The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation they provide a more flexible formulation compared to the classical normal. While these families enjoy attractive formal properties from the probability viewpoint, a practical problem with their usage in applications is the possibility that the maximum likelihood estimate of the parameter which regulates skewness diverges. This situation has vanishing probability for increasing sample size, but for finite samples it occurs with non-negligible probability, and its occurrence has unpleasant effects on the inferential process. Methods for overcoming this problem have been put forward both in the classical and in the Bayesian formulation, but their applicability is restricted to simple situations. We formulate a proposal based on the idea of penalized likelihood, which has connections with some of the existing methods, but it applies more generally, including the multivariate case.

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