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  • Author or Editor: Rolando Cavazos-Cadena x
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Abstract  

Motivated by results in Rotnitzky et al. (2000), a family of parametrizations of the location-scale skew-normal model is introduced, and it is shown that, under each member of this class, the hypothesis H 0: λ = 0 is invariant, where λ is the asymmetry parameter. Using the trace of the inverse variance matrix associated to a generalized gradient as a selection index, a subclass of optimal parametrizations is identified, and it is proved that a slight variant of Azzalini’s centred parametrization is optimal. Next, via an arbitrary optimal parametrization, a simple derivation of the limit behavior of maximum likelihood estimators is given under H 0, and the asymptotic distribution of the corresponding likelihood ratio statistic for this composite hypothesis is determined.

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Authors: Rolando Cavazos-Cadena and Daniel Hernández-Hernández

Abstract  

This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central limit theorem.

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