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  • 1 Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo COAH, 25315 México
  • 2 Centro de Invastigación en Matemáticas A. C., Apartado Postal 402, Guanajuato, GTO, 36240 México
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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 H0: 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 H0, and the asymptotic distribution of the corresponding likelihood ratio statistic for this composite hypothesis is determined.