Robust Mahalanobis distances obtained using the 'multout' and 'fast-mcd' methods

• Autorzy: Bartkowiak A.
• Języki publikacji: EN

Abstrakty

EN

Robust Mahalanobis distances play an essential role in detecting outliers. The robustness is obtained by using for evaluations a robust covariance matrix. We consider two methods of constructing a robust covariance matrix: (i) the 'fast-mcd' (minimum covariance determinant) method proposed by Rousseeuw and van Driessen [14] and (ii) the hybrid method 'multout' proposed by Rocke and Woodruff [12]. The methods are investigated considering six benchmark data sets containing outliers and one medical data set (liver disorders). Both methods yield similar results, though some discrepancies are observed in two of the analyzed benchmark data sets, namely in the 'bushfire' and 'stack-loss' data.

Słowa kluczowe

EN

Mahalanobis distances; robust covariances; outliers

• Wydawca: Nałęcz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences ; Elsevier
• Czasopismo: Biocybernetics and Biomedical Engineering
• Rocznik: 2005
• Tom: Vol. 25, no. 1
• Strony: 7--21
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Bartkowiak A.

• Institute of Computer Science, University of Wrocław, ul. Przesmyckiego 20, 51-151 Wrocław, Poland,

Bibliografia

• [1] Atkinson A.C.: Fast, very robust methods for the detection of multiple outliers, JASA 89, 1329-1339.
• [2] Barnett V., Lewis T.: Outliers in Statistical Data, 3rd Edition, Wiley, Chichester 1994.
• [3] Bartkowiak A.: A semi-stochastic grand tour for identifying outliers and finding a clean subset Biometrical Letters 38, 2001, 1, 11-31.
• [4] Bartkowiak A., Szustalewicz A.: Outliers - finding and classifying which genuine and which spurious Computational Statistics 15, 2000, 1, 3-12.
• [5] Billor N., Hadi A.S. and Velleman P.F.: BACON: blocked adaptive computationally eficient outlier nominators, Computational Statistics & Data Analysis 34, 2000, 3, 279-298.
• [6] Daudin J.J., Duby C. and Trecourt P.: Stability of Principal Component Analysis Studied by the Bootstrap Method, Statistics 19, 1988, 241-258.
• [7] Hardin J. and Rocke D. M.: The distribution of Robust Distances. Report Sept. 1999. http://www.cipic.ucdavis.edu/dmrocke/preprints.html, 1-36.
• [8] Hawkins D.M., Bradu D., Kass G.V.: Location of several outliers in multiple regression using elemental subsets, Technometrics 26, 1984, 197-208.
• [9] Mardia K., Kent J., Bibby J.: Multivariate Analysis, Academic Press, London 1979.
• [10] Maruzabal J. and Munoz A.: On the visualization of outliers via selforganizing maps, J. Of Computational and Graphical Statistics 6, 1997, 355-382.
• [11] Rasmussen C. E.: The Infinite Gaussian Mixture Model. In: S.A. Solla, T.K. Leen and K.-R. Muller (eds), Advances in Neural Information Processing Systems 12, MIT 2000, 554-560.
• [12] Rocke D.M., Woodruff D.L.: Identification of outliers in multivariate data, JASA 91, 1996, 435, 1047-1061.
• [13] Rousseeuw P.J., Leroy A.: Robust regression and outliers detection, Wiley, New York, 1987.
• [14] Rousseeuw P.J., van Driessen K.: A fast algorithm for the minimum covariance determinant estimator Technometrics 41, 1999, 212-223.
• [15] Ruppert D., Carrol R.J.: Trimmed least squares estimation in the linear model, JASA 75 1980, 828-838.