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A matrix formula for the skewness of maximum likelihood estimators

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  • Patriota, Alexandre G.
  • Cordeiro, Gauss M.

Abstract

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model.

Suggested Citation

  • Patriota, Alexandre G. & Cordeiro, Gauss M., 2011. "A matrix formula for the skewness of maximum likelihood estimators," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 529-537, April.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:4:p:529-537
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    References listed on IDEAS

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    1. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.
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    Cited by:

    1. Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.

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