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A Test on a Specific Set of Outlier Candidates in a Linear Model

선형모형에서 특정 이상치 후보군에 대한 검정

  • Seo, Han Son (Department of Applied Statistics, Konkuk University) ;
  • Yoon, Min (Department of Statistics, Pukyong National University)
  • 서한손 (건국대학교 응용통계학과) ;
  • 윤민 (부경대학교 통계학과)
  • Received : 2014.01.02
  • Accepted : 2014.03.20
  • Published : 2014.04.30

Abstract

An exact distribution of the test statistic to test for multiple outlier candidates does not generally exist; therefore, tests of individual outliers (or tests using simulated critical-values) are usually conducted instead of testing for groups of outliers. This article is on procedures to test outlying observations. We suggest a method that can be applied to arbitrary observations or multiple outlier candidates detected by an outlier detecting method. A Monte Carlo study performance is used to compare the proposed method with others.

이상치 후보군을 검정할 때 일반적으로 정확한 검정 통계량의 분포가 존재하지 않는다. 이에 따라 전체 관찰치군에 대한 검정대신 개별 관찰치에 대한 검정을 수행하거나 실험에 의해 계산된 유의값을 사용하여 이상치 가설검정을 수행한다. 본 연구에서는 임의의 관찰치 집단 또는 이상치 탐지절차에 따라 이상치 후보로 탐지된 특정 관찰치 집단의 이상치 여부를 검정하는 방법을 제시한다. 제시된 방법은 기존의 이상치 탐지기법에서 사용되는 검정방법과 모의실험을 통해 검정력을 비교한다.

Keywords

References

  1. Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data, 3rd Edition, Wiley, Chichester, UK.
  2. Brown, R. L., Durbin, J. and Evans, J. M. (1975). Techniques for testing the consistency of regression relations over time, Journal of the Royal Statistical Society, Series B, 37, 149-163.
  3. Gentleman, J. F. and Wilk, M. B. (1975). Detecting outliers.II.Supplementing The Direct Analysis of Residuals, Biometrics, 31, 387-410. https://doi.org/10.2307/2529428
  4. Hadi, A. S. and Simonoff, J. S. (1993). Procedures for the identification of multiple outliers in linear models, Journal of the American Statistical Association, 88, 1264-1272. https://doi.org/10.1080/01621459.1993.10476407
  5. Hawkins, D. M. (1980). Identification of Outliers, Chapman and Hall, New York.
  6. Huber, P. J. (1973). Robust regression: Asymptotics, conjectures and Monte Carlo, Annals of Statistics, 1, 799-821. https://doi.org/10.1214/aos/1176342503
  7. Kianifard, F. and Swallow, W. H. (1989). Using recursive residuals, calculated on adaptively-ordered observations, to identify outliers in linear regression, Biometrics, 45, 571-585. https://doi.org/10.2307/2531498
  8. Kianifard, F. and Swallow, W. H. (1990). A Monte Carlo comparison of five procedures for identifying outliers in linear regression, Communications in Statistics - Theory and Methods, 19, 1913-1938. https://doi.org/10.1080/03610929008830300
  9. Marasinghe, M. G. (1985). A multistage procedure for detecting several outliers in linear regression, Tech- nometrics, 27, 395-399.
  10. Pena, D. and Yohai, V. J. (1995). The detection of influential subsets in linear regression by using an influence matrix, Journal of the Royal Statistical Society, Series B, 57, 145-156.
  11. Plackett, R. L. (1950). Some theorems in least squares, Biometrika, 37, 149-157. https://doi.org/10.1093/biomet/37.1-2.149
  12. Rousseeuw, P. J. (1984). Least median of squares regression, Journal of the American Statistical Association, 79, 871-880. https://doi.org/10.1080/01621459.1984.10477105
  13. Rousseeuw, P. J. (1985). Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, G., Vincze, I., Wertz, W. (Eds.), Mathematical Statistics and Applications, B, Reidel, Dordrecht, 283-297.
  14. Sebert, D. M., Montgomery, D. C. and Rollier, D. (1998). A clustering algorithm for identifying multiple outliers in linear regression, Computational Statistics and Data Analysis, 27, 461-484. https://doi.org/10.1016/S0167-9473(98)00021-8
  15. Swallow, W. H. and Kianifard, F. (1996). Using robust scale estimates in detecting multiple outliers in linear regression, Biometrics, 52, 545-556. https://doi.org/10.2307/2532894
  16. Yohai, V. J. (1987). High breakdown-point and high efficiency robust estimates for regression, The Annals of Statistics, 15, 642-656. https://doi.org/10.1214/aos/1176350366

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