Bias reduction of maximum likelihood estimates for a modified skew-normal distribution

ABSTRACT

This paper presents a modified skew-normal (SN) model that contains the normal model as a special case. Unlike the usual SN model, the Fisher information matrix of the proposed model is always non-singular. Despite of this desirable property for the regular asymptotic inference, as with the SN model, in the considered model the divergence of the maximum likelihood estimator (MLE) of the skewness parameter may occur with positive probability in samples with moderate sizes. As a solution to this problem, a modified score function is used for the estimation of the skewness parameter. It is proved that the modified MLE is always finite. The quasi-likelihood approach is considered to build confidence intervals. When the model includes location and scale parameters, the proposed method is combined with the unmodified maximum likelihood estimates of these parameters.

KEYWORDS:

• Modified skew-normal
• non-singular information matrix
• monotone likelihood
• modified likelihood
• modified score
• bias prevention

Acknowledgments

The authors acknowledge helpful comments and suggestions by the referees which substantially improved the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of R.B. Arellano-Valle was supported by FONDECYT (Chile) 1120121. The research of H.W. Gómez was supported by FONDECYT (Chile) 1130495.