Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A study on robust regression estimators in heteroscedastic error models

  • Son, Nayeong (Department of Statistics, Ewha Womans University) ;
  • Kim, Mijeong (Department of Statistics, Ewha Womans University)
  • Received : 2017.09.01
  • Accepted : 2017.09.18
  • Published : 2017.09.30
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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 butterfly-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.

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References

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