Bias prevention of maximum likelihood estimates for skew-normal-Cauchy distribution

Abstract

This work focuses on the so-called skew-normal-Cauchy distribution, which is a convenient alternative to the skew-normal distribution for modeling data in presence of asymmetries. A stochastic representation and further nice properties of the skew-normal-Cauchy distribution are considered. Despite these desirable properties, the skew-normal-Cauchy model presents similar peculiarities as the skew-normal model in estimating the skewness parameter. Particularly, in finite samples, the maximum likelihood estimator of the shape parameter can be infinite with positive probability. In order to address this problem a modified score function is used. Also a quasi-likelihood approach is considered for obtaining confidence intervals. BMI data of elite athletes are used to illustrate this issue.

Keywords:

• Bias reduction
• Modified likelihood
• Quasi-likelihood
• Skewness
• Skew-normal-Cauchy distribution

Acknowledgments

Arellano-Valle’s research was supported by Grant FONDECYT (Chile) 1150325.