The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Robust Response Transformation Using Outlier Detection in Regression Model

회귀모형에서 이상치 검색을 이용한 로버스트 변수변환방법

  • Seo, Han-Son (Department of Applied Statistics, Konkuk University) ;
  • Lee, Ga-Yoen (Strategy & Planning Team, Okcashbag Service) ;
  • Yoon, Min (Department of Statistics, Pukyong National University)
  • 서한손 (건국대학교 응용통계학과) ;
  • 이가연 (오케이캐시백 서비스 전략기획팀) ;
  • 윤민 (부경대학교 통계학과)
  • Received : 20111000
  • Accepted : 20111100
  • Published : 2012.02.29
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Abstract

Transforming response variable is a general tool to adapt data to a linear regression model. However, it is well known that response transformations in linear regression are very sensitive to one or a few outliers. Many methods have been suggested to develop transformations that will not be influenced by potential outliers. Recently Cheng (2005) suggested to using a trimmed likelihood estimator based on the idea of the least trimmed squares estimator(LTS). However, the method requires presetting the number of outliers and needs many computations. A new method is proposed, that can solve the problems addressed and improve the robustness of the estimates. The method uses a stepwise procedure, suggested by Hadi and Simonoff (1993), to detect outliers that determine response transformations.

선형회귀모형에서 자료를 모형에 적합시킬 때 일반적으로 반응변수 변환을 시도하지만 적절한 변환함수의 결정은 몇개의 이상치들에 민감하게 반응한다는 것이 잘 알려져 있다. 이에 따라 이상치에 영향을 받지 않는 변수변환 방법들이 연구, 개발되고 있으나 최근에 Cheng (2005)에 의해 최소절사제곱추정치에 기반을 둔 절사 우도추정치 방법처럼 이상치의 숫자를 미리 정해야한다거나 많은 계산량이 필요하다는 단점들을 갖고 있다. 본 논문에서는 그와 같은 문제점을 해결하고 추정치의 강건성을 개선하는 새로운 방법을 제안하며 제안된 방법에서는 반응변수 변환에 따른 이상치 탐색법에 있어서 Hadi와 Simonoff (1993)가 제시한 단계적 절차를 응용, 적용한다.

Keywords

References

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