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Robust Statistics

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Handbook of Computational Statistics

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

The first example involves the real data given in Table 25.1 which are the results of an interlaboratory test. The boxplots are shown in Fig. 25.1 where the dotted line denotes the mean of the observations and the solid line the median.

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References

  • Adrover, J.: Minimax bias-robust estimation of the dispersion matrix of multivariate distributions. Ann. Stat. 26, 2301–2320 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Andrews, D.F., Bickel, P.J., Hampel, F.R., Rogers, W.H., Tukey, J.W.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton, NJ (1972)

    MATH  Google Scholar 

  • Atkinson, A.C.: Fast very robust methods for the detection of multiple outliers. J. Am. Stat. Assoc. 89, 1329–1339 (1994)

    Article  MATH  Google Scholar 

  • Barme-Delcroix, M.-F., Gather, U.: An isobar-surfaces approach to multidimensional outlier-proneness. Technical Report 20, Sonderforschungsbereich 475, University of Dortmund, Dortmund, Germany (2000)

    Google Scholar 

  • Barnett, V., Lewis, T.: Outliers in Statistical Data. (3rd edn.), Wiley, New York, (1994)

    MATH  Google Scholar 

  • Bartlett, M.S.: The effect of non-normality on the t-distribution. Proc. Camb. Phil. Soc. 31, 223–231 (1935)

    Article  Google Scholar 

  • Becker, C., Gather, U.: The masking breakdown point of multivariate outlier identification rules. J. Am. Stat. Assoc. 94:947–955 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Becker, C., Gather, U.: The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules. Comput. Stat. Data Anal. 36, 119–127 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Bednarski, T.: Fréchet differentiability and robust estimation. In: Mandl, P., Husková, M. (eds) Asymptotic Statistics: Proceedings of the Fifth Prague Symposium, Springer Lecture Notes, pp. 49–58. Springer (1993)

    Google Scholar 

  • Bednarski, T., Clarke, B.R.: On locally uniform expansions of regular functionals. Discussiones Mathematicae Algebra Stoch. Meth. 18, 155–165 (1998)

    MathSciNet  MATH  Google Scholar 

  • Bednarski, T., Clarke, B.R., Kolkiewicz, W.: Statistical expansions and locally uniform Fréchet differentiability. J. Aust. Math. Soc. 50, 88–97 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Bernholt, T., Fischer, P.: The complexity of computing the mcd-estimator. Technical Report 45, Sonderforschungsbereich 475, University of Dortmund, Dortmund, Germany (2001)

    Google Scholar 

  • Berrendero, J.R., Zamar, R.H.: Maximum bias curves for robust regression with non-elliptical regressors. Ann. Stat. 29, 224–251 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Box, G.E.P.: Non-normality and test on variance. Biometrika 40, 318–335 (1953)

    MathSciNet  MATH  Google Scholar 

  • Box, G.E.P., Andersen, S.L.: Permutation theory in the derivation of robust criteria and the study of departures from assumption. J. Roy. Stat. Soc. B 17, 1–34 (1955)

    MATH  Google Scholar 

  • Caroni, C., Prescott, P.: Sequential application of wilk’s multivariate outlier test. Appl. Stat. 41, 355–364 (1992)

    Article  MATH  Google Scholar 

  • Chang, H., McKean, J.W., Narjano, J.D., Sheather, S.J.: High-breakdown rank regression. J. Am. Stat. Assoc. 94(445):205–219 (1999)

    Article  MATH  Google Scholar 

  • Clarke, B.R.: Uniqueness and Fréchet differentiability of functional solutions to maximum likelihood type equations. Ann. Stat. 11, 1196–1205 (1983)

    MATH  Google Scholar 

  • Cohen, M.: The background of configural polysampling: a historical perspective. In: Morgenthaler, S., Tukey, J.W. (eds) Configural Polysampling: A Route to Practical Robustness, Chap. 2. Wiley, New York (1991)

    Google Scholar 

  • Croux, C., Dehon, C.: Robust linear discriminant analysis using S-estimators. Can. J. Stat. 29, 473–492 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Croux, C., Haesbroeck, G.: Principal components analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87, 603–618 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Croux, C., Rousseeuw, P.J.: Time-efficient algorithms for two highly robust estimators of scale. In: Dodge, Y., Whittaker, J.C. (eds) Computational Statistics, vol. 1, pp. 411–428. Physica, Heidelberg (1992)

    Google Scholar 

  • Davies, P.L.: Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices. Ann. Stat. 15, 1269–1292 (1987)

    Article  MATH  Google Scholar 

  • Davies, P.L.: The asymptotics of Rousseeuw’s minimum volume ellipsoid. Ann. Stat. 20, 1828–1843 (1992a)

    Article  MATH  Google Scholar 

  • Davies, P.L.: Aspects of robust linear regression. Ann. Stat. 21, 1843–1899 (1993)

    Article  MATH  Google Scholar 

  • Davies, P.L.: Data features. Stat. Neerl. 49, 185–245 (1995)

    MATH  Google Scholar 

  • Davies, P.L.: On locally uniformly linearizable high breakdown location and scale functionals. Ann. Stat. 26, 1103–1125 (1998)

    Article  MATH  Google Scholar 

  • Davies, P.L.: The one-way table. J. Stat. Plann. Infer. 122, 3–13 (2004)

    Article  MATH  Google Scholar 

  • Davies, P.L., Gather, U.: The identification of multiple outliers (with discussion). J. Am. Stat. Assoc. 88, 782–801 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Dietel, G.: Global location and dispersion functionals. PhD thesis, University of Essen (1993)

    Google Scholar 

  • Donoho, D.L.: Breakdown properties of multivariate location estimators. PhD thesis, Department of Statistics, Harvard University, Harvard, Mass (1982)

    Google Scholar 

  • Donoho, D.L., Gasko, M.: Breakdown properties of location estimates based on halfspace depth and project outlyingness. Ann. Stat. 20, 1803–1827 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Donoho, D.L., Huber, P.J.: The notion of breakdown point. In: Bickel, P.J., Doksum, K.A., Hodges, J.L. Jr. (eds) A Festschrift for Erich L. Lehmann, pp. 157–184, Wadsworth, Belmont, California (1983)

    Google Scholar 

  • Eddington, A.S.: Stellar Movements and the Structure of the Universe. Macmillan, New York (1914)

    Google Scholar 

  • Edelsbrunner, H., Souvaine, D.: Computing median-of-squares regression lines and guided topological sweep. J. Am. Stat. Assoc. 85, 115–119 (1990)

    Article  MATH  Google Scholar 

  • Ellis, S.P.: Instability of least squares, least absolute deviation and least median of squares linear regression. Stat. Sci. 13(4), 337–350 (1998)

    Article  MATH  Google Scholar 

  • Fernholz, L.T.: Von Mises Calculus for Statistical Functionals. Number 19 in Lecture Notes in Statistics. Springer, New York (1983)

    Google Scholar 

  • Fisher, R.A.: A mathematical examination of the methods of determining the accuracy of an observation by the mean error and the mean square error. Mon. Not. Roy. Astron. Soc. 80, 758–770 (1920)

    Google Scholar 

  • Fisher, R.A.: The Design of Experiments, Oliver and Boyd, Edinburgh and London (1935)

    Google Scholar 

  • Gather, U.: Modelling the occurrence of multiple outliers. All. Stat. Arch. 74, 413–428 (1990)

    Google Scholar 

  • Gather, U., Hilker, T.: A note on tyler’s modification of the MAD for the stahel-donoho estimator. Ann. Stat. 25, 2024–2026 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Gather, U., Kuhnt, S., Pawlitschko, J.: Concepts of outlyingness for various data structures. In: Misra, J.C. (eds.) Industrial Mathematics and Statistics. pp. 545–585. Narosa Publishing House, New Delhi (2003)

    Google Scholar 

  • Gather, U., Schultze, V.: Robust estimation of scale of an exponential distribution. Stat. Neerl. 53, 327–341 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Gayen, A.K.: The distribution of the variance ratio in random samples of any size drawn from non-normal universe. Biometrika 37, 236–255 (1950)

    MathSciNet  MATH  Google Scholar 

  • Geary, R.C.: The distribution of ’student’s’ ratio for non-normal samples. J. Roy. Stat. Soc. Suppl. 3, 178–184 (1936)

    Article  MATH  Google Scholar 

  • Geary, R.C.: Testing for normality. Biometrika 34, 209–242 (1947)

    MathSciNet  MATH  Google Scholar 

  • Gervini, D., Yohai, V.J.: A class of robust and fully efficient regression estimators. Ann. Stat. 30(2), 583–616 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Gnanadesikan, R., Kettenring, J.R.: Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics 28, 81–124 (1972)

    Article  Google Scholar 

  • Hadi, A.S.: A modification of a method for the detection of outliers in multivariate samples. J. Roy. Stat. Soc. B 56, 393–396 (1994)

    MATH  Google Scholar 

  • Hadi, A.S., Simonoff, J.S.: Procedures for the identification of multiple outliers in linear models. J. Am. Stat. Assoc. 88, 1264–1272 (1997)

    Article  MathSciNet  Google Scholar 

  • Hampel, F.R.: Contributions to the theory of robust estimation. PhD thesis, University of California, Berkeley (1968)

    Google Scholar 

  • Hampel, F.R.: Beyond location parameters: Robust concepts and methods (with discussion). In: Proceedings of the 40th Session of the ISI, vol. 46, Book 1, pp. 375–391 (1975)

    Google Scholar 

  • Hampel, F.R.: The breakdown points of the mean combined with some rejection rules. Technometrics 27, 95–107 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions, Wiley, New York (1986)

    MATH  Google Scholar 

  • Hawkins, D.M.: Identification of outliers, Chapman and Hall, London (1980)

    MATH  Google Scholar 

  • Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Stat. 35, 73–101 (1964)

    Article  MATH  Google Scholar 

  • Huber, P.J.: Robust statistical procedures. In: Regional Conference Series in Applied Mathematics No. 27, Society for Industrial and Applied Mathematics, Philadelphia, Penn (1977)

    Google Scholar 

  • Huber, P.J.: Robust Statistics, Wiley, New York (1981)

    MATH  Google Scholar 

  • Huber, P.J.: Finite sample breakdown points of m- and p-estimators. Ann. Stat. 12, 119–126 (1984)

    Article  MATH  Google Scholar 

  • Huber, P.J.: Robustness: Where are we now? Student 1, 75–86 (1995)

    Google Scholar 

  • Kent, J.T., Tyler, D.E.: Redescending M-estimates of multivariate location and scatter. Ann. Stat. 19, 2102–2119 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Kent, J.T., Tyler, D.E.: Constrained M-estimation for multivariate location and scatter. Ann. Stat. 24, 1346–137 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Liu, R.Y., Parelius, J.M., Singh, K.: Multivariate analysis by data depth: descriptive statistics, graphics and inference. Ann. Stat. 27, 783–840 (1999)

    MathSciNet  MATH  Google Scholar 

  • Lopuhaä, H.P.: On the relation between S-estimators and M-estimators of multivariate location and covariance. Ann. Stat. 19, 229–248 (1989)

    Article  Google Scholar 

  • Lopuhaä, H.P.: Multivariate τ-estimators for location and scatter. Can. J. Stat. 19, 307–321 (1991)

    Article  MATH  Google Scholar 

  • Lopuhaä, H.P., Rousseeuw, P.J.: Breakdown properties of affine equivariant estimators of multivariate location and covariance matrices. Ann. Stat. 19, 229–248 (1991)

    Article  MATH  Google Scholar 

  • Marazzi, A.: Algorithms, Routines, and S- Functions for Robust Statistics. Chapman and Hall, New York (1992)

    Google Scholar 

  • Maronna, R.A.: Robust M-estimators of multivariate location and scatter. Ann. Stat. 4(1), 51–67 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  • Maronna, R.A., Stahel, W.A., Yohai, V.J.: Bias-robust estimators of multivariate scatter based on projections. J. Multivariate Anal. 42, 141–161 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Maronna, R.A., Yohai, V.J.: Asymptotic behavior of general M-estimates for regression and scale with random carriers. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 58, 7–20 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • Maronna, R.A., Yohai, V.J.: Bias-robust estimates of regression based on projections. Ann. Stat. 21(2), 965–990 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Martin, R.D., Yohai, V.J., Zamar, R.H.: Min-max bias robust regression. Ann. Stat. 17(4), 1608–1630 (1989)

    MathSciNet  MATH  Google Scholar 

  • Martin, R.D., Zamar, R.H.: Bias robust estimation of scale. Ann. Stat. 21(2), 991–1017 (1993a)

    Article  MathSciNet  MATH  Google Scholar 

  • Martin, R.D., Zamar, R.H.: Efficiency constrained bias robust estimation of location. Ann. Stat. 21(1), 338-354 (1993b)

    Article  MathSciNet  MATH  Google Scholar 

  • Mendes, B., Tyler, D.E.: Constrained M-estimates for regression. In: Rieder, H. (eds.) Robust Statistics; Data Analysis and Computer Intensive Methods, number 109 in Lecture Notes in Statistics, pp. 299–320. Springer, New York (1996)

    Chapter  Google Scholar 

  • Neyman, J., Pearson, E.S.: On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Roy. Soc. (London) A 231, 289–337 (1933)

    Google Scholar 

  • Pearson, E.S.: The distribution of frequency constants in small samples from non-normal symmetrical and skew populations. Biometrika 21, 259–286 (1929)

    MATH  Google Scholar 

  • Pearson, E.S.: The analysis of variance in cases of non-normal variation. Biometrika 23, 114–133 (1931)

    Google Scholar 

  • Pearson, E.S., Chandra Sekar, S.: The efficiency of statistical tools and a criterion for the rejection of outlying observations. Biometrika 28, 308–320 (1936)

    Google Scholar 

  • Pollard, D.: Convergence of Stochastic Processes. Springer, New York (1984)

    MATH  Google Scholar 

  • Riedel, M.: On the bias-robustness in the location model i. Statistics 2, 223–233 (1989a)

    Article  MathSciNet  Google Scholar 

  • Riedel, M.: On the bias-robustness in the location model ii. Statistics 2, 235–246 (1989b)

    Article  MathSciNet  Google Scholar 

  • Rieder, H.: Robust Asymptotic Statistics. Springer, Berlin (1994)

    MATH  Google Scholar 

  • Rocke, D.M.: Robustness properties of S-estimators of multivariate location and shape in high dimension. Ann. Stat. 24, 1327–1345 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Rocke, D.M., Woodruff, D.L.: Identification of outliers in multivariate data. J. Am. Stat. Assoc. 91(435), 1047–1061 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Rocke, D.M., Woodruff, D.L.: Robust estimation of multivariate location and shape. J. Stat. Plann. Infer. 91, 245–255 (1997)

    Article  MathSciNet  Google Scholar 

  • Rosner, B.: On the detection of many outliers. Technometrics 17, 221–227 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P.J.: Least median of squares regression. J. Am. Stat. Assoc. 79, 871–880 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P.J.: Multivariate estimation with high breakdown point. In: Grossmann, W., Pflug, C.G., Vincze, I., Wertz, W. (eds) Mathematical Statistics and Applications (Proceedings of the 4th Pannonian Symposium on Mathematical Statistics), vol. B, Reidel, Dordrecht (1985)

    Google Scholar 

  • Rousseeuw, P.J., Croux, C.: Explicit scale estimators with high breakdown point. In: Dodge, Y. (eds.) L 1-Statistical Analysis and Related Methods, pp. 77–92, North Holland, Amsterdam (1992)

    Google Scholar 

  • Rousseeuw, P.J., Croux, C.: Alternatives to the median absolute deviation. J. Am. Stat. Assoc. 88, 1273–1283 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P.J., Croux, C.: The bias of k-step M-estimators. Stat. Probab. Lett. 20, 411–420 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P.J., Hubert, M.: Regression depth. J. Am. Stat. Assoc. 94, 388–402 (1999)

    MathSciNet  MATH  Google Scholar 

  • Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection, Wiley, New York (1987)

    Google Scholar 

  • Rousseeuw, P.J., Van Driesen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212–223 (1999)

    Article  Google Scholar 

  • Rousseeuw, P.J., Van Driesen, K.: An algorithm for positive-breakdown methods based on concentration steps. In: Gaul, W., Opitz, O., Schader, M. (eds.) Data Analysis: Scientific modelling and Practical Application, pp. 335–346. Springer, New York (2000)

    Google Scholar 

  • Rousseeuw, P.J., van Zoomeren, B.C.: Unmasking multivariate outliers and leverage points. J. Am. Stat. Assoc. 85, 633–639 (1990)

    Article  Google Scholar 

  • Rousseeuw, P.J., Yohai, V.J.: Robust regression by means of S-estimators. In: Franke, J.E.A. (eds.) Robust and Nonlinear Time Series Analysis, pp. 256–272, New York. Springer (1984)

    Google Scholar 

  • Scholz, F.W.: Comparison of Optimal Location Estimators. PhD thesis, Department of Statistics, University of California, Berkley (1971)

    Google Scholar 

  • Sheather, S.J., McKean, J.W., Hettmansperger, T.P.: Finite sample stability properties of the least median of squares estimator. J. Stat. Comput. Simul. 58(4), 371–383 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Simonoff, J.S.: A comparison of robust methods and detection of outlier techniques when estimating a location parameter. Comm. Stat. A 13, 813–842 (1984)

    Article  Google Scholar 

  • Simonoff, J.S.: The breakdown and influence properties of outlier rejection-plus-mean procedures. Comm. Stat. A 16, 1749–1760 (1987)

    Article  MathSciNet  Google Scholar 

  • Stahel, W.A.: Breakdown of covariance estimators. Research Report 31, Fachgruppe für Statistik, ETH, Zurich (1981)

    Google Scholar 

  • Staudte, R.G., Sheather, S.J.: Robust Estimation and Testing, Wiley, New York (1990)

    MATH  Google Scholar 

  • Tatsuoka, K.S., Tyler, D.E.: On the uniqueness of S-functionals and M-functionals under non-elliptic distributions. Ann. Stat. 28(4), 1219–1243 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • Terbeck, W., Davies, P.L.: Interactions and outliers in the two-way analysis of variance. Ann. Stat. 26, 1279–1305 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Tietjen, G.L., Moore, R.H.: Some grubbs-type statistics for the detection of several outliers. Technometrics 14, 583–597 (1972)

    Article  Google Scholar 

  • Tukey, J.W.: A survey of sampling from contaminated distributions. In: Olkin, I. (eds.) Contributions to Probability and Statistics. Stanford University Press, Stanford, California (1960)

    Google Scholar 

  • Tukey, J.W.: Mathematics and picturing data. In: Proceedings of International Congress of Mathematicians, Vancouver, vol. 2, pp. 523–531 (1975)

    MathSciNet  Google Scholar 

  • Tukey, J.W.: Exploratory analysis of variance as providing examples of strategic choices. In: Morgenthaler, S., Ronchetti, E., Stahel, W.A. (eds.) New Directions in Statistical Data Analysis and Robustness, Birkhäuser, Basel (1993)

    Google Scholar 

  • Tyler, D.E.: Finite sample breakdown points of projection based multivariate location and scatter statistics. Ann. Stat. 22, 1024–1044 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • von Mises, R.: Sur les fonctions statistiques. In: Conférence de la Réunion Internationale des Mathmaticiens. Gauthier-Villars (1937)

    Google Scholar 

  • Willems, S., Pison, G., Rousseeuw, P.J., Van Aelst, S.: A robust Hotelling test. Metrika 55, 125–138 (2002)

    Google Scholar 

  • Yohai, V.J.: High breakdown point and high efficiency robust estimates for regression. Ann. Stat. 15, 642–656 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  • Yohai, V.J., Maronna, R.A.: The maximum bias of robust covariances. Comm. Stat. Theor. Meth. 19, 3925–3933 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  • Yohai, V.J., Zamar, R.H.: High breakdown point estimates of regression by means of the minimization of an efficient scale. J. Am. Stat. Assoc. 83, 406–413 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Zuo, Y.: Some quantitative relationships between two types of finite sample breakdown points. Stat. Probab. Lett. 51, 369–375 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Zuo, Y., Serfling, R.: General notions of statistical depth function. Ann. Stat. 28, 461–482 (2000a)

    Article  MathSciNet  MATH  Google Scholar 

  • Zuo, Y., Serfling, R.: Structural properties and convergence results for contours of sample statistical depth functions. Ann. Stat. 28, 483–499 (2000b)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Universität Duisburg-Essen, Essen, Germany

    Laurie Davies

  2. Technische Universität Dortmund, Dortmund, Germany

    Ursula Gather

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  1. Laurie Davies
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  2. Ursula Gather
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  1. Dept. Computational & Data, Sciences, George Mason University, University Drive 4400, Fairfax, 22030-4444, Virginia, USA

    James E. Gentle

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. Dept. Socioinformation, Okayama University, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yuichi Mori

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Davies, L., Gather, U. (2012). Robust Statistics. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21551-3_25

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