Minimum profile hellinger distance estimation of semiparametric multiple linear regression models

Abstract

As the most fundamental tool to analyse associations, the semiparametric multiple linear regression model is considered in this work where the error distribution is assumed symmetric but otherwise completely unknown. To handle the common concern about possible outlying observations, especially in the era of big data, we propose a robust estimator of regression coefficients based on Hellinger distance and profiling technique. We prove in theory that the resulting estimator, minimum profile Hellinger distance estimator (MPHDE), is consistent. Its finite-sample performance is examined via both extensive simulation studies and a real data application. Our numerical results demonstrate that the proposed MPHDE has good efficiency and simultaneously is very robust against outlying observations.

Keywords:

• Semiparametric linear regression model
• minimum profile Hellinger distance estimator
• kernel estimator
• identifiability
• efficiency
• robustness

AMS 2020 subject classifications:

• Primary 62F10
• 62G05
• secondary 62G07
• 62G35

Acknowledgments

The authors would also like to thank the Associate Editor and the anonymous referee for their constructive comments.

Disclosure statement

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

Additional information

Funding

The authors acknowledge with gratitude the support for this research via Discovery Grants from Natural Sciences and Engineering Research Council (NSERC) of Canada.