Robust Location and Scale Estimation Based on the Univariate Generalized t (GT) Distribution

Abstract

In this paper, we consider the univariate generalized t (GT) distribution, which is introduced by McDonald and Newey ((1988) Partially adaptive estimation of regression models via the generalized t distribution. Econometric Theory 4:428–457.). We show that the maximum likelihood estimators for the location and the scale parameters of a GT distribution with known shape parameters can provide alternative robust estimators for the location and scale parameters of a data set. We investigate the existence and the uniqueness of the maximum likelihood estimators. We show that the likelihood function can be unimodal or multimodal depending on the different choices of the shape parameters.

Keywords:

• Univariate GT distribution
• Box and Tiao (BT) distribution
• Generalized gamma (GG) distribution
• Maximum likelihood estimation
• M-estimation
• Robustness
• Influence function

Acknowledgments

We would like to thank an anonymous referee and the associate editor for their valuable comments and suggestions which have improved this work.