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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Communicated by István Berkes
Dedicated to the memory of Don José María Morelos y Pavón
This work was supported by the PSF Organization under Grant No. 2007-4, and by CONA-CYT under Grant 105657 /CB2008
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Cavazos-Cadena, R., González-Farías, G.M. Optimal reparametrization and large sample likelihood inference for the location-scale skew-normal model. Period Math Hung 64, 181–211 (2012). https://doi.org/10.1007/s10998-012-5259-4
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DOI: https://doi.org/10.1007/s10998-012-5259-4