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A study on robust regression estimators in heteroscedastic error models
Journal of the Korean Data & Information Science Society 2017;28:1191-204
Published online September 30, 2017
© 2017 Korean Data & Information Science Society.

Nayeong Son1 · Mijeong Kim2

12Department of Statistics, Ewha Womans University
Correspondence to: Mijeong Kim
Assistant professor, Department of Statistics, Ewha Womans University, 52, Ewhayeodae-gil, Seodaemun-gu, Seoul, Republic of Korea. E-mail: m.kim@ewha.ac.kr
Received September 1, 2017; Revised September 15, 2017; Accepted September 18, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Weighted least squares (WLS) estimation is often easily used for the data with heteroscedastic errors because it is intuitive and computationally inexpensive. However, WLS estimator is less robust to a few outliers and sometimes it may be inefficient. In order to overcome robustness problems, Box-Cox transformation, Huber's M estimation, bisquare estimation, and Yohai's MM estimation have been proposed. Also, more efficient estimations than WLS have been suggested such as Bayesian methods (Cepeda and Achcar, 2009) and semiparametric methods (Kim and Ma, 2012) in heteroscedastic error models. Recently, Çelik (2015) proposed the weight methods applicable to the heteroscedasticity patterns including buttery-distributed residuals and megaphone-shaped residuals. In this paper, we review heteroscedastic regression estimators related to robust or efficient estimation and describe their properties. Also, we analyze cost data of U.S. Electricity Producers in 1955 using the methods discussed in the paper.
Keywords : Bayesian heteroscedastic regression model, heteroscedastic regression, robust estimators, semiparametric efficient estimators, weighting absolute centered external variable