Robust explicit estimators using the power-weighted repeated medians

Abstract

This paper consists of two parts. The first part of the paper is to propose an explicit robust estimation method for the regression coefficients in simple linear regression based on the power-weighted repeated medians technique that has a tuning constant for dealing with the trade-offs between efficiency and robustness. We then investigate the lower and upper bounds of the finite-sample breakdown point of the proposed method. The second part of the paper is to show that based on the linearization of the cumulative distribution function, the proposed method can be applied to obtain robust parameter estimators for the Weibull and Birnbaum-Saunders distributions that are commonly used in both reliability and survival analysis. Numerical studies demonstrate that the proposed method performs well in a manner that is approximately comparable with the ordinary least squares method, whereas it is far superior in the presence of data contamination that occurs frequently in practice.

Keywords:

• Finite-sample breakdown point
• linear model
• repeated median
• robustness
• weighted median

Mathematical subject classifications:

• 62F10
• 62J05

Acknowledgments

The authors truly appreciate the valuable comments from two anonymous referees which led to a great improvement in our work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of Professor Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1091319). The work of Professor Gao was supported by National Science Foundation of China Grant No. 72104020 and China Postdoctoral Science Foundation, No. 15 Special Fund (In-Station), Grant No. 2022T150044. The work of Dr. Min Wang was partially supported by the Internal Research Awards (INTRA), UTSA program from the Vice President for Research, Economic Development, and Knowledge Enterprise at the University of Texas at San Antonio.