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A Hybrid Algorithm for Identifying Multiple Outlers in Linear Regression

Kim, Bu-yong   (Department of Statistics, Sookmyung Women′s University  ); Kim, Hee-young   (Strategy and Innovation Dept., Kookmin Credit Card Co. Ltd  );
  • 초록

    This article is concerned with an effective algorithm for the identification of multiple outliers in linear regression. It proposes a hybrid algorithm which employs the least median of squares estimator, instead of the least squares estimator, to construct an Initial clean subset in the stepwise forward search scheme. The performance of the proposed algorithm is evaluated and compared with the existing competitor via an extensive Monte Carlo simulation. The algorithm appears to be superior to the competitor for the most of scenarios explored in the simulation study. Particularly it copes with the masking problem quite well. In addition, the orthogonal decomposition and Its updating techniques are considered to improve the computational efficiency and numerical stability of the algorithm.


  • 참고문헌 (11)

    1. Procedures for the Identification of Multiple Outliers in Linear Models , Hadi, A. S.;Simonoff, J. S. , Journal of the American Statistical Association / v.88,pp.1264-1272,
    2. Testing for a Single Outlier in Simple Linear Regression , Tietjen, G. L.;Moore, R. H.;Beckman, R. J. , Technometrics / v.15,pp.717-721,
    3. Unmasking Multivariate Outliers and Leverage Points , Rousseeuw, P. J.;Zomeren, B. C. , Journal of the American Statistical Association / v.85,pp.633-639,
    4. $L_{\infty}$-estimation based Algorithm for the Least Median of Squares Estimator , Kim, B. Y. , The Korean Communications in Statistics / v.3,pp.299-307,
    5. A Multistage Procedure for Detecting Several Outliers in Linear Regression , Marasinghe, M. G. , Technometrics / v.27,pp.395-399,
    6. A Comparative Analysis of Multiple Outlier Detection Procedures in the Linear Regression Model , Wisnowski, J. W.;Montgomery, D. C.;Simpson, J. R. , Computational Statistics and Data Analysis / v.36,pp.351-382,
    7. Equivariant, Monotonic, 50% Breakdown Estimators , Basset, Jr. G. W. , The American Statistician / v.45,pp.135-137,
    8. A Monte Carlo Comparison of Five Procedures for Identifying Outliers in Linear Regression , Kianifard, F.;Swallow, W. H. , Commun. Statist.-Theory Meth. / v.19,pp.1913-1938,
    9. Rousseeuw, P. J.;Leroy, A. M. , Robust Regression nad Outlier Detection / v.,pp.,
    10. Least Median of Squares Regression , Rousseeuw, P. J. , Journal of the American Statistical Association / v.79,pp.871-880,
    11. Improvements in Computational Efficiency and Accuracy of an Algorithm for the Identification of Regression Outliers , Kim, B. Y.;Kim, S. B. , Journal of Natural Sciences / v.8,pp.135-142,
  • 이 논문을 인용한 문헌 (2)

    1. 2004. "" 한국통계학회 논문집 = Communications of the Korean Statistical Society, 11(3): 485~494     
    2. Kim, Bu-Yong 2011. "A Criterion for the Selection of Principal Components in the Robust Principal Component Regression" 한국통계학회 논문집 = Communications of the Korean Statistical Society, 18(6): 761~770     

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