Asymptotic normality of estimators for parameters of a multivariate skew-normal distribution

ABSTRACT

In this paper, asymptotic normality is established for the parameters of the multivariate skew-normal distribution under two parametrizations. Also, an analytic expression and an asymptotic normal law are derived for the skewness vector of the skew-normal distribution. The estimates are derived using the method of moments. Convergence to the asymptotic distributions is examined both computationally and in a simulation experiment.

KEYWORDS:

• Asymptotic normality
• multivariate cumulants
• multivariate moments, multivariate skewness
• skew-normal distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E20
• 62H10
• 65C60

Acknowledgments

The authors are also thankful to the editors and the anonymous referees for their helpful and constructive comments that greatly contributed to improving the final version of the paper.

Additional information

Funding

The authors are thankful for the financial support of the Estonian Science Foundation [grant number 9127] and the research project IUT34-5.