The Accuracy of Elemental Set Approximations for Regression

References

• Atkinson , A. C. 1988 . Transformations Unmasked . Technometrics , 30 : 311 – 318 .
   Web of Science ®Google Scholar
• Atkinson , A. C. 1986 . Masking Unmasked . Biometrika , 73 : 29 – 37 .
   Web of Science ®Google Scholar
• Atkinson , A. C. and Weisberg , S. 1991 . “ Simulated Annealing for the Detection of Multiple Outliers Using Least Squares and Least Median of Squares Fitting ” . In Directions in Robust Statistics and Diagnostics: Part I , Edited by: Stahel , W. and Weisberg , S. 7 – 20 . New York : Springer-Verlag .
   Google Scholar
• Bradu , D. and Hawkins , D. M. Sample Size Requirements for Multiple Outlier Location Techniques Based on Elemental Sets . Computational Statistics and Data Analysis , (in press)
   Web of Science ®Google Scholar
• Cook , R. D. and Hawkins , D. M. 1990 . Outliers Everywhere''–Comment on “Unmasking Multivariate Outliers and Leverage Points . Journal of the American Statistical Association , 85 : 640 – 644 . by P. J. Rousseeuw and B. C. van Zomeren
   Web of Science ®Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust Statistics: The Approach Based on Influence Functions , New York : John Wiley .
   Google Scholar
• Hawkins , D. M. , Bradu , D. and Kass , G. V. 1984 . Location of Several Outliers in Multiple Regression Data Using Elemental Sets . Technometrics , 26 : 197 – 208 .
   Web of Science ®Google Scholar
• Hawkins , D. M. and Simonoff , J. S. 1991 . High Breakdown Regression and Multivariate Estimation submitted to Applied Statistics
   Google Scholar
• Hettmansperger , T. P. and Sheather , S. J. 1992 . A Cautionary Note on the Method of Least Median Squares . The American Statistician , 46 : 79 – 83 .
   Web of Science ®Google Scholar
• Huber , P. J. 1981 . Robust Statistics , New York : John Wiley .
   Google Scholar
• Joss , J. and Marazzi , A. 1989 . Probabilistic Algorithms for Least Median of Squares Regression . Computational Statistics and Data Analysis , 9 : 123 – 133 .
   Web of Science ®Google Scholar
• Krasker , W. S. and Welsch , R. E. 1982 . Efficient Bounded Influence Regression Estimation . Journal of the American Statistical Association , 77 : 595 – 604 .
   Web of Science ®Google Scholar
• Lopuhaä , H P. 1991 . “ Breakdown Point and Asymptotic Properties of Multivariate S-Estimators and τ-Estimators–A Summary ” . In Directions in Robust Statistics and Diagnostics: Part I , Edited by: Stahel , W. and Weisberg , S. 167 – 182 . New York : Springer-Verlag .
   Google Scholar
• Marazzi , A. 1991 . “ Algorithms and Programs for Robust Linear Regression ” . In Directions in Robust Statistics and Diagnostics: Part I , Edited by: Stahel , W. and Weisberg , S. 183 – 199 . New York : Springer-Verlag .
   Google Scholar
• Portnoy , S. 1987 . “ Using Regression Fractiles to Identify Outliers ” . In Statistical Data Analysis Based on the LI-Norm and Related Methods , Edited by: Dodge , Y. Amsterdam : North-Holland .
   Google Scholar
• Rousseeuw , P. J. 1985 . “ Multivariate Estimation With High Breakdown Point ” . In Mathematical Statistics and Applications , Edited by: Grossman , W. , Pflug , G. , Vincze , I. and Wertz , W. Vol. B , 283 – 297 . Dordrecht : Reidel Publishing .
   Google Scholar
• Rousseeuw , P. J. 1984 . Least-Median of Squares Regression . Journal of the American Statistical Association , 79 : 871 – 880 .
   Web of Science ®Google Scholar
• Rousseeuw , P. J. 1983 . Regression Techniques With High Breakdown Point . IMS Bulletin , 12 : 155
   Google Scholar
• Rousseeuw , P. J. and Bassett , G. W. Jr . 1991 . “ Robustness of the p-Subset Algorithm for Regression With High Breakdown Point ” . In Directions in Robust Statistics and Diagnostics: Part II , Edited by: Stahel , W. and Weisberg , S. 185 – 194 . New York : Springer-Verlag .
   Google Scholar
• Rousseeuw , P. J. and Leroy , A. M. 1986 . Robust Regression and Outlier Detection , New York : John Wiley .
   Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. 1991 . “ Robust Distances: Simulations and Cutoff Values ” . In Directions in Robust Statistics and Diagnostics: Part II , Edited by: Stahel , W. and Weisberg , S. 195 – 203 . New York : Springer-Verlag .
   Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. 1990 . Unmasking Multivariate Outliers and Leverage Points . Journal of the American Statistical Association , 85 : 633 – 639 .
   Web of Science ®Google Scholar
• Ruppert , D. and Simpson , D. G. 1990 . Comment on “Unmasking Multivariate Outliers and Leverage Points” . Journal of the American Statistical Association , 85 : 644 – 646 . by P. J. Rousseeuw and B. C. van Zomeren
   Web of Science ®Google Scholar
• Simpson , D. G. , Ruppert , D. and Carroll , R. J. 1992 . On One-Step GM Estimators and Stability of Inferences in Linear Regression . Journal of the American Statistical Association , 86 : 439 – 450 .
   Google Scholar
• Steele , J. M. and Steiger , W. L. 1986 . Algorithms and Complexity for Least Median of Squares Regression . Discrete Applied Mathematics , 14 : 93 – 100 .
   Web of Science ®Google Scholar
• Stromberg , A. J. 1991 . Computing the Exact Value of the Least Median of Squares Estimate in Multiple Linear Regression , University of Minnesota, School of Statistics . Technical Report No. 561
   Google Scholar
• Theil , H. 1950 . A Rank-Invariant Method of Linear and Polynomial Regression Analysis, Parts 1–3 . Nederlandsche Akademie voor Wetenschap Proceedings Series A , 53 : 386 – 392 . 521 – 525 . 1397 – 1412 .
   Google Scholar
• Tichavsky , P. 1991 . Algorithms for and Geometrical Characterization of Solutions in the LMS and LTS Linear Regression . Computational Statistics Quarterly , 6 : 139 – 151 .
   Google Scholar
• Yohai , V. J. 1987 . High Breakdown Point and High Efficiency Robust Estimates for regression . The Annals of Statistics , 15 : 642 – 656 .
   Web of Science ®Google Scholar
• Yohai , V. J. and Zamar , R. H. 1988 . High Breakdown-Point Estimates of Regression by Means of Minimization of an Efficient Scale . Journal of the American Statistical Association , 83 : 406 – 413 .
   Web of Science ®Google Scholar