A biased-robust regression technique for the combined outlier-multicollinearity problem

References

• Askin , R.G. and Montgomery , D.C. 1980 . Augmented Robust Estimators . Technometrics , 22 : 333 – 341 .
   Web of Science ®Google Scholar
• Askin , R.G. and Montgomery , D.C. 1984 . An Analysis of Constrained Robust Regression Estimators . Naval Research Logistics Quarterly , 31 : 283 – 296 .
   Google Scholar
• Belsley , D.A. , Kuh , E. and Welsch , R.E. 1980 . Regression Diagnostics: Identifying Influential Data and Sources of Collinearity , New York : Wiley: .
   Google Scholar
• Coakley , C.W. and Hettmansperger , T.P. 1993 . A Bounded Influence, High Breakdown, Efficient Regression Estimator . Journal of the American Statistical Association , 88 : 872 – 880 .
   Web of Science ®Google Scholar
• Cook , R.D. and Hawkins , D.M. 1990 . 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. 1973 . Robust Estimation: A Condensed Partial Survey . Zeitschrift für Wahrscheinlichkeitsthiorie und Verwandte Gebiete , 27 : 87 – 104 .
   Web of Science ®Google Scholar
• Handshin , E. , Schweppe , F. , Kohlas , J. and Fiechter , A. 1975 . Bad Data Analysis for Power System State Estimation . IEEE Transactions on Power Apparatus Systems , PAS-94 : 329 – 337 .
   Google Scholar
• Hawkins , D.W. , 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
• Hettmansperger , T.P. and Sheather , S.J. 1991 . A Cautionary Note on the Method of Least Median Squares . The American Statistician , 46 : 79 – 83 .
   Web of Science ®Google Scholar
• Hoerl , A.E. and Kennard , R.W. 1970a . Ridge Regression: Biased Estimation for Non-orthogonal Problems . Technometrics , 12 : 55 – 67 .
   Web of Science ®Google Scholar
• Hoerl , A.E. and Kennard , R.W. 1970b . Ridge Regression: Applications to Non-orthogonal Problems . Technometrics , 12 : 69 – 82 .
   Web of Science ®Google Scholar
• Hoerl , A.E. and Kennard , R.W. 1976 . Ridge Regression: Iterative Estimation of the Biasing Parameter . Communications in Statistics , A5 : 77 – 88 .
   Google Scholar
• Holland , P.W. 1973 . Weighted Ridge Regression: Combining Ridge and Robust Regression Methods . NBER Working Paper Series , 11 : 1 – 19 . Working Paper
   Google Scholar
• Huber , P.J. 1977 . “ Robust Covariances ” . In Statistical Decision Theory and Related Topics , Edited by: Gupta , . and Moore , . Vol. 2 , 165 – 191 . New York : Academic Press .
   Google Scholar
• Huber , P.J. 1981 . Robust Statistics , New York : Wiley .
   Google Scholar
• Krasker , W.S. and Welsh , R.E. 1982 . Efficient Bounded-Influence Regression Estimation . Journal of the American Statistical Association , 77 : 595 – 603 .
   Web of Science ®Google Scholar
• Lawrence , K.D. and Marsh , L.C. 1984 . Robust Ridge Estimation Methods for Predicting U.S. Coal Mining Fatalities . Communications in Statistics-Theory and Methods , 13 : 139 – 149 .
   Web of Science ®Google Scholar
• Marazzi , A. 1993 . Algorithms, Routines, and S Functions for Robust Statistics , Pacific Grove, California : Wadsworth and Brooks/Cole .
   Google Scholar
• Maronna , R.A. 1976 . Robust M-estimators of Multivariate Location and Scatter . Annals of Statistics , 4 : 51 – 67 .
   Web of Science ®Google Scholar
• Marquardt , D.W. 1970 . Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation . Technometrics , 12 : 591 – 612 .
   Web of Science ®Google Scholar
• Mason , R.L. and Gunst , R.F. 1985 . Outlier-Induced Collinearities . Technometrics , 27 : 401 – 407 .
   Web of Science ®Google Scholar
• Pariente S. Welsch R. E. Ridge and Robust Regression Using Parametric Linear Programming Alfred P. Sloan School of Management 1977 Working Paper, MIT
   Google Scholar
• Pfaffenberger , R.C. and Dielman , T.E. 1985 . A Comparison of Robust Ridge Estimators . Business Economics Section Proceedings of the American Statistical Association . 1985 . pp. 631 – 635 .
   Google Scholar
• Rousseeuw , P.J. 1983 . “ Multivariate Estimation with High Breakdown Point ” . In Mathematical Statistics and Applications , Edited by: Grossman , W. , Pflug , G. , Vincze , I. and Wertz , W. 283 – 297 . Netherlands : Reidel: Dordrecht . B
   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. and Van Zomeren , B.C. 1990 . Unmasking Multivariate Outliers and Leverage Points . Journal of the American Statistical Association , 85 : 633 – 651 .
   Web of Science ®Google Scholar
• Rousseeuw , P.J. and Yohai , V.J. 1984 . “ Robust Regression by Means of S-Esti-mators ” . In Robust and Nonlinear Time Series Analysis , Edited by: Franke , J. , Hardie , W. and Martin , D. 256 – 272 . Heidelberg, , Germany : Springer-Verlag .
   Google Scholar
• S-Plus , . 1994 . S-PLUS Reference Manual , Seattle : Statistical Sciences .
   Google Scholar
• Simonoff , J.S. 1991 . “ General Approaches to Stepwise Identification of Unusual Values in Data Analysis ” . In Directions in Robust Statistics and Diagnostics , Edited by: Stahel , W. and Weisberg , S. 223 – 242 . Heidelberg, , Germany : Springer-Verlag: . Part II
   Google Scholar
• Simpson , D.G. , Ruppert , D. and Carroll , R.J. 1992 . On One-Step GM Estimates and Stability of Influences in Linear Regression . Journal of the American Statistical Association , 87 : 439 – 450 .
   Web of Science ®Google Scholar
• Simpson J. R. New Methods and Comparative Evaluations for Robust and Biased-Robust Regression Estimation Department of Industrial and Management Systems Engineering, Arizona State University 1995 unpublished Ph. D. dissertation
   Google Scholar
• Stahel , W.A. 1981 . Breakdown of Covariance Estimators , Zurich : ETH . Research Report 3.1, Fachgruppe fÜr Statistik,
   Google Scholar
• Walker , E. 1984 . Influence, Collinearity, and Robust Estimation in Regression , Virginia Polytechnic Institute. . unpublished Ph.D. dissertation, Department of Statistics
   Google Scholar
• Walker , E. and Birch , J.B. 1988 . Influence Measures in Ridge Regression . Technometrics , 30 : 221 – 227 .
   Web of Science ®Google Scholar