Heuristic Search Algorithms for the Minimum Volume Ellipsoid

References

• Andrews , D. F. , Bickel , P. J. , Hampel , F. R. , Huber , P. J. , Rogers , W. H. and Tukey , J. W. 1972 . Robust Estimates of Location: Survey and Advances , Princeton : Princeton University Press .
   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
• Campbell , N. A. 1980 . “Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation” . Applied Statistics , 29 : 231 – 237 .
   Google Scholar
• Campbell , N. A. 1982 . “Robust Procedures in Multivariate Analysis I: Robust Canonical Variate Analysis” . Applied Statistics , 31 : 1 – 8 .
   Web of Science ®Google Scholar
• Cook , R. D. and Hawkins , D. M. 1990 . “Comment” . Journal of the American Statistical Association , 85 : 640 – 644 .
   Web of Science ®Google Scholar
• Davies , P. L. 1987 . “Asymptotic Behavior of 5-Estimators of Multivariate Location Parameters and Dispersion Matrices” . The Annals of Statistics , 15 : 1269 – 1292 .
   Web of Science ®Google Scholar
• Davis , L. 1991 . Handbook of Genetic Algorithms , New York : Van Nostrand Reinhold .
   Google Scholar
• Devlin , S. J. , Gnanadesikan , R. and Kettenring , J. R. 1981 . “Robust Estimation of Dispersion Matrices and Principal Components” . Journal of the American Statistical Association , 76 : 354 – 362 .
   Web of Science ®Google Scholar
• Donoho , D. L. 1982 . “Breakdown Properties of Multivariate Location Estimators” , Harvard University, Dept. of Statistics . unpublished PhD qualifying paper
   Google Scholar
• Donoho , D. L. and Huber , P. J. 1983 . “The Notion of Breakdown Point” . In A Festschrift for Erich L. Lehmann , Edited by: Bickel , P. J. , Doksum , K. A. and Hodges , J. L. 157 – 184 . Belmont , CA : Wadsworth .
   Google Scholar
• Faigle , U. and Kern , W. 1989 . “Some Convergence Results for Probabilistic Tabu Search” , University of Twente, The Netherlands, Dept. of Applied Mathematics . working paper
   Google Scholar
• Fox , B. L. 1991 . “Eliminating a Pathology of Simulated Annealing” , University of Colorado, Denver, Dept. of Mathematics . working paper
   Google Scholar
• Glover , F. 1989 . “Tabu Search–Part I” . ORSA Journal on Computing , 1 : 190 – 206 .
   Google Scholar
• Glover , F. 1990 . “Tabu Search–Part II” . ORSA Journal on Computing , 2 : 4 – 32 .
   Google Scholar
• Glover , F. and Laguna , M. 1990 . “Target Analysis to Improve Tabu Search” , University of Texas, Austin, Graduate Program in Operations Research . Technical Report ORP89-21
   Google Scholar
• Goldberg , D. E. 1989 . Genetic Algorithms in Search Optimization and Machine Learning , Reading , MA : Addison-Wesley .
   Google Scholar
• Hajek , B. 1988 . “Cooling Schedules for Optimal Annealing” . Mathematics of Operations Research , 13 : 311 – 329 .
   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
• Hartl , R. F. 1991 . “A Global Convergence Proof for a Class of Genetic Algorithms” , Vienna University of Technology, Institute of Econometrics, Operations Research and Systems Theory . working paper
   Google Scholar
• Huber , P. J. 1981 . Robust Statistics , New York : John Wiley .
   Google Scholar
• Huber , P. J. 1985 . “Projection Pursuit” . The Annals of Statistics , 13 : 435 – 475 .
   Web of Science ®Google Scholar
• Johnson , D. S. , Aragon , C. R. , McGeoch , L. A. and Schevon , C. 1989 . “Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning” . Operations Research , 37 : 865 – 892 .
   Web of Science ®Google Scholar
• Kempthorne , P. J. and Mendel , M. B. 1990 . “Comment” . Journal of the American Statistical Association , 85 : 647 – 648 .
   Web of Science ®Google Scholar
• Laguna , M. , Barnes , J. W. and Glover , F. 1990 . “Scheduling Jobs with Linear Delay Penalties and Sequence Dependent Setup Costs and Times Using Tabu Search” , University of Texas, Austin, Dept. of Mechanical Engineering . Research Report
   Google Scholar
• Liepins , G. E. and Baluja , S. 1991 . “apGA: An Adaptive Parallel Genetic Algorithm” , Oak Ridge National Laboratory . working paper
   Google Scholar
• Liepins , G. E. and Vose , M. D. 1990 . “Characterizing Crossover in Genetic Algorithms” , Oak Ridge National Laboratory . working paper
   Google Scholar
• Lopuhaä , H. P. 1989 . “On the Relation Between S-Estimators and M-Estimators of Multivariate Location and Covariance” . The Annals of Statistics , 17 : 1662 – 1683 .
   Web of Science ®Google Scholar
• Lopuhaä , H. P. and Rousseeuw , P. J. 1991 . “Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices” . The Annals of Statistics , 19 : 229 – 248 .
   Web of Science ®Google Scholar
• Lundy , M. and Mees , A. 1986 . “Convergence of an Annealing Algorithm” . Math Programming , 34 : 111 – 124 .
   Web of Science ®Google Scholar
• Maronna , R. A. 1976 . “Robust M-Estimators of Multivariate Location and Scatter” . The Annals of Statistics , 4 : 51 – 67 .
   Web of Science ®Google Scholar
• Portnoy , S. 1987 . “Using Regression Fractiles to Identify Outliers” . In Statistical Data Analysis Based on the L₁-Norm , Edited by: Dodge , Y. 345 – 356 . Amsterdam : North-Holland .
   Google Scholar
• Rousseeuw , P. J. 1985 . “Multivariate Estimation With High Breakdown Point” . In Mathematical Statistics and Applications , Edited by: Grossmann , W. , Pflug , G. , Vincze , I. and Werz , W. Volume B , 283 – 297 . Dordrecht : Reidel .
   Google Scholar
• Rousseeuw , P. J. and Leroy , A. M. 1987 . Robust Regression and Outlier Detection , New York : John Wiley .
   Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. C. 1990a . “Unmasking Multivariate Outliers and Leverage Points” . Journal of the American Statistical Association , 85 : 633 – 639 .
   Web of Science ®Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. C. 1990b . “Rejoinder” . Journal of the American Statistical Association , 85 : 648 – 651 .
   Google Scholar
• Rousseeuw , P. J. and van Zomeren , B. C. 1991 . “Robust Distances: Simulations and Cutoff Values” . In Directions in Robust Statistics and Diagnostics Part II , Edited by: Stahel , W. and Weisberg , S. 195 – 204 . New York : Springer-Verlag .
   Google Scholar
• Ruppert , D. and Simpson , D. G. 1990 . “Comment” . Journal of the American Statistical Association , 85 : 644 – 646 .
   Web of Science ®Google Scholar
• Schaffer , J. D. 1987 . “Some Effects of Selection Procedures on Hyperplane Sampling by Genetic Algorithms” . In Genetic Algorithms and Simulated Annealing , Edited by: Davis , L. London : Pitman .
   Google Scholar
• Skorin-Kapov , J. 1991 . “Extensions of a Tabu Search Adaptation to the Quadratic Assignment Problem” , State University of New York at Stony Brook, W. A. Harriman School for Management and Policy . Working Paper HAR-90-006
   Google Scholar
• Stahel , W. A. 1981 . “Robuste Schätzungen: Infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen” , Zurich : Eidgenössishe Technische Hochschule . unpublished PhD thesis
   Google Scholar
• Statistical Sciences . 1991 . S-Plus for DOS Reference Manual , Seattle : Author .
   Google Scholar
• Syswerda , G. “Uniform Crossover in Genetic Algorithms” . Proceedings of the Third International Conference on Genetic Algorithms . Edited by: Shaffer , J. pp. 2 – 9 . San Mateo , CA : Morgan Kaufmann Publishers .
   Google Scholar
• Tanese , R. “Distributed Genetic Algorithms” . Proceedings of the Third International Conference on Genetic Algorithms . Edited by: Shaffer , J. pp. 434 – 439 . San Mateo , CA : Morgan Kaufmann Publishers .
   Google Scholar
• Tyler , D. E. 1983 . “Robustness and Efficiency Properties of Scatter Matrices” . Biometrika , 70 : 411 – 420 .
   Web of Science ®Google Scholar
• Tyler , D. E. 1991 . “Some Issues in the Robust Estimation of Multivariate Location and Scatter” . In Directions in Robust Statistics and Diagnostics Part II , Edited by: Stahel , W. and Weisberg , S. 327 – 336 . New York : Springer-Verlag .
   Google Scholar
• Whitley , D. “The GENTITOR Algorithm and Selection Pressure: Why Rank-Based Allocation of Reproductive Trials is Best” . Proceedings of the Third International Conference on Genetic Algorithms . Edited by: Shaffer , J. pp. 116 – 121 . San Mateo , CA : Morgan Kaufmann Publishers .
   Google Scholar
• Woodruff , D. L. and Rocke , D. M. 1991 . “Computation of the Minimum Volume Ellipsoid Estimator Using Heuristic Search” , University of California, Davis, Graduate School of Management . Technical Report
   Google Scholar
• Woodruff , D. L. and Zemel , E. 1990 . “Hashing Vectors for Tabu Search” unpublished article submitted to Annals of OR.
   Google Scholar