Investigation of finite-sample properties of robust location and scale estimators

Abstract

When the experimental data set is contaminated, we usually employ robust alternatives to common location and scale estimators such as the sample median and Hodges-Lehmann estimators for location and the sample median absolute deviation and Shamos estimators for scale. It is well known that these estimators have high positive asymptotic breakdown points and are Fisher-consistent as the sample size tends to infinity. To the best of our knowledge, the finite-sample properties of these estimators, depending on the sample size, have not well been studied in the literature. In this paper, we fill this gap by providing their closed-form finite-sample breakdown points and calculating the unbiasing factors and relative efficiencies of the robust estimators through the extensive Monte Carlo simulations up to the sample size 100. The numerical study shows that the unbiasing factor improves the finite-sample performance significantly. In addition, we provide the predicted values for the unbiasing factors obtained by using the least squares method which can be used for the case of sample size more than 100.

Keywords:

• Breakdown
• Unbiasedness
• robustness
• Relative efficiency

Acknowledgments

The authors greatly appreciate the reviewers for their thoughtful comments and suggestions, which have significantly improved the quality of this manuscript.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. NRF-2017R1A2B4004169).