One-step M-estimators: Jones and Faddy's skewed t-distribution

Abstract

One-step M (OSM)-estimator needs some initial/preliminary estimates at the beginning of the calculation process. In this study, we propose to use new initial estimates for the calculation of the OSM-estimator. We consider simple location and simple linear regression models when the distribution of the error terms is Jones and Faddy's skewed t. Monte-Carlo simulation study shows that the OSM estimator(s) based on the proposed initial estimates is/are more efficient than the OSM estimator(s) based on the traditional initial estimates especially for the skewed cases. We also analyze some real data sets taken from the literature at the end of the paper.

Keywords:

• one-step M-estimator
• modified likelihood
• regression
• robustness
• efficiency

Acknowledgements

We thank the editor and the referees for their valuable comments and suggestions that greatly improved the paper.