Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Least clipped absolute deviation for robust regression using skipped median

  • Hao Li (Department of Statistics, Hankuk University of Foreign Studies) ;
  • Seokho Lee (Department of Statistics, Hankuk University of Foreign Studies)
  • Received : 2022.07.28
  • Accepted : 2022.09.26
  • Published : 2023.03.31
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Abstract

Skipped median is more robust than median when outliers are not symmetrically distributed. In this work, we propose a novel algorithm to estimate the skipped median. The idea of skipped median and the new algorithm are extended to regression problem, which is called least clipped absolute deviation (LCAD). Since our proposed algorithm for nonconvex LCAD optimization makes use of convex least absolute deviation (LAD) procedure as a subroutine, regularizations developed for LAD can be directly applied, without modification, to LCAD as well. Numerical studies demonstrate that skipped median and LCAD are useful and outperform their counterparts, median and LAD, when outliers intervene asymmetrically. Some extensions of the idea for skipped median and LCAD are discussed.

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Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003956).

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