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List of publications

Books as Author

  • Mathematische Methoden für Ökonomen - 3nd edition (with R. Dyckerhoff and C. Scheicher). 603 pages, Berlin (Springer) 2018.
  • Statistik kompakt. Basiswissen für Ökonomen und Ingenieure (with Tatjana Lange). 114 pages, Berlin (Springer) 2017.
  • Beschreibende Statistik und Wirtschaftsstatistik, 4th edition (with F. Schmid). 254 pages, Berlin (Springer) 2009.
  • Wahrscheinlichkeitsrechnung und schließende Statistik, 4th edition (with F. Schmid). 347 pages, Berlin (Springer) 2011.
  • Multivariate Dispersion, Central Regions and Depth: The Lift Zonoid Approach. Lecture Notes in Statistics. 291 Seiten, Berlin (Springer) 2002.
  • Stochastic Orders and Applications, A Classified Bibliography. (with M. Scarsini). 379 pages, Berlin (Springer) 1993. MR 94g:60001. [Introduction as .PDF]
  • Continuous Location of Transportation Networks. 158 pages, Berlin (Springer) 1987. Zbl. 618.90026.
  • Entscheidungsregeln bei Risiko: Multivariate stochastische Dominanz. 172 pages, Berlin (Springer) 1982. Zbl. 497.62009.
  • Optimale Transportnetze. Zur Bestimmung ihres kostengünstigsten Standorts bei gegebener Nachfrage. 142 pages, Berlin (Springer) 1976. MR 53.5:12553.

Books as Editor

  • Wolf Krumbholz: Statistische Qualitaetskontrolle (with Wilfried Seidel). 268 pages, Hamburg (Kovac) 2009. Link
  • Decision Theory and Decision Systems
    (Volume 52 of the Annals of Operations Research, with M. Schader).
    249 pages, Basel (Baltzer) 1994. MR 95d:90007. [Preface as .PDF]
  • Operations Research '92 (with A. Karmann, M. Schader and G. Uebe). 581 pages, Heidelberg (Physica) 1993. MR 94b:90007.
  • Stochastic Orders and Decision under Risk (with M. Scarsini). 392 pages, Hayward, California (Institute of Mathematical Statistics) 1991. MR 93g:60003.
  • Operations Research and Economic Theory, Essays in Honor of M. J. Beckmann (with H. Hauptmann and W. Krelle). 378 pages, Berlin (Springer) 1984. MR 85i:90004.


  • Representative endowments and uniform Gini orderings of multi-attribute welfare. Journal of Economic Inequality 2022. Available online:
  • Choosing among notions of multivariate depth statistics (with Pavlo Mozharovskyi). Statistical Science 37 (2022), 348-368.
  • Commentary on 'From unidimensional to multidimensional inequality: A review'. METRON 78 (2020), 51-54. Available online:
  • Computing the Oja median in R: The Package OjaNP (with Daniel Fischer, Jyrki Möttönen, Klaus Nordhausen, Oleksii Pokotylo, and Daniel Vogel). Journal of Statistical Software 92 (2020), Issue 8.
  • Fast computation of Tukey trimmed regions and median in dimension p>2 (with Xiaohui Liu and Pavlo Mozharovskyi). Journal of Computational and Graphical Statistics 28 (2019), 682-697.
  • A polarization index for overlapping groups (with Chiara Gigliarano and Daniel Nowak). Review of Income and Wealth 65 (2019), 712-735. [Full Paper as .PDF]
  • Classification with the pot-pot plot (with Oleksii Pokotylo). Statistical Papers 60 (2019), 553-581. DOI 10.1007/s00362-016-0854-8.  [Full Paper as .PDF]
  • Fast DD-classification of functional data
    (with Pavlo Mozharovskyi). Statistical Papers 58(2017), 1055–1089. [Full Paper as arXiv:1403.1158] (The final publication is available at
  • Computation of the Oja Median by Bounded Search (with Oleksii Pokotylo). Klaus Nordhausen and Sara Taskinen, eds., Modern Nonparametric, Robust and Multivariate Methods, Festschrift in Honour of Hannu Oja. New York (Springer) 2015. 185-203. [Full Paper as .PDF
    (The final publication is available at
  • Discussion of 'Multivariate functional outlier detection' by Mia Hubert, Peter Rousseeuw and Pieter Segaert 
    Statistical Methods and Applications 24 (2015), 203 - 207 [Full Paper as .PDF]
    (The final publication is available at
  • A general solution for robust linear programs with distortion risk constraints (with Pavel Bazovkin) 
    Annals of Operations Research 229:103 (2015) [Full Paper as .PDF] DOI 10.1007/s10479-015-1786-8
    (The final publication is available at
  • Classifying real-world data with the DDα-procedure (with Pavlo Mozharovskyi and Tatjana Lange) 
    Advances in Data Analysis and Classification 9 (2015), 287 - 314 [Full Paper as .PDF
    (The final publication is available at
  • Stochastic linear programming with a distortion risk constraint (with Pavel Bazovkin) 
    OR Spectrum 36 (2014), 949 - 969 [Full Paper as .PDF]
    (The final publication is available at
  • DDα-classification of asymmetric and fat-tailed data (with Tatjana Lange and Pavlo Mozharovskyi)
    In: M. Spiliopoulou, L. Schmidt-Thieme, R. Janning, eds., Data Analysis, Machine Learning and Knowledge Discovery, Berlin (Springer) 2014, 71-78 [Full Paper as .PDF]
    (The final publication is available at
  • Fast nonparametric classification based on data depth (with Tatjana Lange and Pavlo Mozharovskyi)
    Statistical Papers 55 (2014), 49-69 [Full Paper as .PDF]
    (The final publication is available at
  • Effektivnaia glubinnaia klassifikatsiia s pomoshchiu proektivnogo invarianta klassovoi prinadlezhnosti (Efficient depth-based classification using a projective invariant of class membership; with T. Lange and P. Mozharovskyi)
    Upravliaiushchie Sistemy I Mashiny (Control Systems and Computers) 2013, 47-58
    [Full Paper as .PDF]
  • Depth statistics
    C. Becker, R. Fried, S. Kuhnt , eds., Robustness and Complex Data Structures, Festschrift in Honour of Ursula Gather, Berlin (Springer) 2013, 17-34. [Full Paper as .PDF]
  • Semiparametric modeling of age-specfic variations in income related health inequalities (with Martin Siegel). Health Economics 23(2014), 870-878 [Full Paper as .PDF]
  • An exact algorithm for weighted-mean trimmed regions in any dimension (with Pavel Bazovkin)
    Journal of Statistical Software 47 (2012), 1-29.  [Full Paper as .PDF]
  • Weighted-mean regions of a probability distribution (with R. Dyckerhoff) [Full Paper as .PDF]
    This is the author's version of a work that was subsequently published in Statistics and Probability Letters 82 (2012), 318-325.
  • Weighted-mean trimming of multivariate data (with R. Dyckerhoff) [Full Paper as .PDF]
    This is the author's version of a work that was subsequently published in Journal of Multivariate Analysis 102 (2011), 405-421.
  • The effect of infrequent trading on detecting price jumps (with Frowin C. Schulz)
    AStA: Advances in Statistical Analysis 95 (2011), 27-58. [Full Paper as .PDF]
  • Wege in die Zukunft (mit Göran Kauermann). In: H. Grohmann, W. Krämer, A. Steger, eds., Statistik in Deutschland, Berlin (Springer) 2011, 69-76. [Full Paper as .PDF]
  • A general approach to depth for functional data (with Yulia Polyakova). In: G. D'Amico, G. Di Biase, J. Janssen, R. Manca (eds.) Proceedings ASMDA 2011, 1022-1029. See also arXiv:1208.1981.
  • Computing zonoid trimmed regions in dimension d > 2 (with Tatjana Lange and Pavel Bazovkin) [Full Paper as .PDF]
    This is the author's version of a work that was subsequently published in Computational Statistics and Data Analysis 53 (2009), 2500 - 2510.
  • A comparison of recent procedures in Weibull mixture testing (with Lars Haferkamp).
    C.H. Skiadas, ed., Advances in Data Analysis, Boston (Birkhäuser), 2009, 219-226. [Full Paper as .PDF]
    (The final publication is available at
  • Constructing indices of multivariate polarization (with Chiara Gigliarano).
    Journal of Economic Inequality 7 (2009) 435 - 460. [Full Paper as .PDF]
    (The final publication is available at
  • Measuring middle-class decline in one and many attributes (with Chiara Gigliarano).Quaderno di Ricerca n. 333, Università Politecnica delle Marche (2009). [Full Paper as .PDF]
  • Statistik. Schwerpunktstichwort in: Das neue Lexikon der Betriebswirtschaftslehre (S.G. Häberle, ed.). München (Oldenbourg), 2008. [Full Paper as .PDF]
  • Attenuation of relative poverty by taxes and subsidies (with Christoph Scheicher).
    METRON LXVI (2008), 265 - 283 [Full Paper as .PDF]
  • Homogeneity testing in a Weibull mixture model (with C. Scheicher).Measuring
    Statistical Papers (April 2008), Vol. 49 Issue 2, 315-332. 18p [Full Paper as .PDF]
    (The final publication is available at
  • Size and Power of Recent Tests for Homogeneity in Exponential Mixtures (with Lars Haferkamp). Communications in Statistics - Simulation and Computation 36.3 (2007), 493-504.([Full Paper as .PDF] Author Posting. (c) Taylor & Francis, 2007. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Communications in Statistics - Simulation and Computation, Volume 36 Issue 3, May 2007. doi:10.1080/03610910701212074)
  • Multivariate Lorenz dominance based on zonoids (with G. Koshevoy).
    AStA: Advances in Statistical Analysis 91 (2007), 57-76. [Full Paper as .PDF]
    (The final publication is available at
  • Data analysis and classification with the zonoid depth (with R. Hoberg).
    In: R. Liu, R. Serfling, D. Souvaine, eds., Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications, American Mathematical Society (2006), 49 - 59. [Full Paper as .PDF]
  • Can Markov-regime switching models improve power price forecasts? Evidence for German daily power prices (with P. Kosater).
    Applied Energy 83 (2006), 943 - 958. [Full Paper as .PDF]
  • Studienaufbau und Studienerfolg von Kölner Volks- und Betriebswirten im Grundstudium (with A. Savin).
    Das Hochschulwesen 53 (2005), 144 - 150. [Full Paper as .PDF]
  • Studienaufbau und Studienerfolg von Kölner Volks- und Betriebswirten im Hauptstudium (with A. Savin).
    Das Hochschulwesen 53 (2005), 181 - 187. [Full Paper as .PDF]
  • Restricted Lorenz dominance of economic inequality in one and many dimensions.
    Journal of Economic Inequality 2 (2004), 89-103. [Abstract as .PDF] ([Full Paper as .PDF] : The final publication is available at
  • Introduction: The geometry of data.
    Allgemeines Statistisches Archiv 88 (2004), 133-135. [Full Paper as .PDF]
    (The final publication is available at
  • Classification based on data depth (with Richard Hoberg).
    Bulletin of the ISI 54th Session (2003). [.PDF]
  • Central regions and dependency.
    Methodology and Computing in Applied Probability 5 (2003), 5-21. [Full paper as .PDF] : This is a preprint of an article accepted for publication in "Methodology and Computing in Applied Probability" ©2003 John Wiley & Sons.)
  • Mixture models in econometric duration analysis. Applied Stochastic Models in Business and Industry 19 (2003), 91-104.[Full Paper as .PDF] : This is a preprint of an article accepted for publication in "Applied Stochastic Models in Business and Industry" ©2003 John Wiley & Sons.)
  • Multidimensional indices and orders of diversity.
    Community Ecology 2 (2001), 137-143. [Full Paper as .PDF
  • Testing for homogeneity in an exponential mixture model (with Wilfried Seidel).
    Australian and New Zealand Journal of Statistics 43 (2001). [Full Paper as .PDF
  • A cautionary note on likelihood ratio tests in mixture models (with Wilfried Seidel und Manfred Alker).
    Annals of the Institute of Statistical Mathematics 52 (2000), 481-487. [Full paper as .PDF]
  • Likelihood ratio tests based on subglobal optimization: A power comparison in exponential mixture models (with Wilfried Seidel and Manfred Alker).
    Statistical Papers 41 (2000), 85-98. [Full paper as .PDF]
  • Depth of hyperplanes and related statistics (with Gleb Koshevoy).
    In: W. Gaul, M. Schader, eds., Mathematische Methoden der Wirtschaftswissenschaften. Heidelberg (Physica) 1999, 162-171. [Abstract]
  • Measuring multivariate concentration: A geometric approach (with Gleb Koshevoy).
    Allgemeines Statistisches Archiv 83 (1999), 173-189. [Abstract]
  • Welfare means and equalizing transfers (with Pietro Muliere).
    Metron 56 (1998), 11-52. [Abstract]
  • Specification analysis in mixed hazard models and a test of crossing survival functions (with Tomas Philipson).
    Statistical Papers 40 (1999), 37-54. [Abstract]
  • Lift zonoids, random convex hulls and the variability of random vectors (with Gleb Koshevoy).
    Bernoulli 4 (1998), 377-399. [Full paper as .PDF]
  • Zonoid trimming for multivariate distributions (with Gleb Koshevoy).
    Annals of Statistics 25 (1997), 1998-2017. [Full paper as .PDF]
  • Orthant orderings of discrete random vectors (with Rainer Dyckerhoff).
    Journal of Statistical Planning and Inference 62 (1997), 193-205. [Full paper as .PDF]
  • A bounding procedure for multiattribute expected utility (with Hartmut Holz).
    In: E. Gruber / A. Tangian, eds., Constructing Scalar-Valued Objective Functions. Berlin (Springer) 1997, 153-165. [Abstract]
  • Multivariate Gini indices (with Gleb Koshevoy).
    Journal of Multivariate Analysis 60 (1997), 252-276. [Full paper as .PDF]
  • De minimis and equity in risk.
    Theory and Decision 42 (1997), 215-233. [Full paper as .PDF]
  • Inequality indices and the starshaped principle of transfers (with Pietro Muliere).
    Statistical Papers 37 (1996), 343-364. [Abstract]  
    Reprinted in: The Economics of Income Inequality, edited by R. A. Becker, Edward Elgar Publ., 2013.
  • Zonoid data depth: Theory and computation (with Rainer Dyckerhoff and Gleb Koshevoy). In: A. Prat. ed.,
    COMPSTAT 1996, Heidelberg (Physica) 1996, 235-240. [Full Paper as .PDF
  • The Lorenz zonoid of a multivariate distribution (with Gleb Koshevoy).
    Journal of the American Statistical Association 91 (1996), 873-882. [Abstract]
  • An algorithm for multivariate weak stochastic dominance (with Hartmut Holz and Rainer Dyckerhoff).
    In: F. Faulbaum/W. Bandilla eds., SoftStat '95, Stuttgart (Lucius) 1996. [Abstract]
  • Testing whether two distributions are stochastically ordered or not.
    In: H. Rinne/B. Rüger/H. Strecker eds., Grundlagen der Statistik und ihre Anwendungen, Festschrift für Kurt Weichselberger, Heidelberg (Physica) 1995, 149--155. [PDF]
  • An interactive decision procedure with multiple attributes under risk (with H. Holz).
    Annals of Operations Research 52 (1994), 151--170. [Full Paper as .PDF
  • Majorization in economic disparity measures.
    Linear Algebra and Its Applications 199 (1994), 91--114. MR CMP 94 12. [Full Paper as .PDF
  • Multidimensional welfarisms.
    In: W. Eichhorn ed., Models and Measurement of Welfare and Inequality, Berlin (Springer) 1994, 808--820. [Abstract]
  • Stochastic dominance with nonadditive probabilities (with R. Dyckerhoff).
    Zeitschrift für Operations Research 37 (1993), 231--256. MR 94g:90007. [Full Paper as .PDF]
  • Location of a spatially extended facility with respect to a point.
    In: T. R. Lakshmanan/P. Nijkamp eds., Structure and Change in the Space Economy, Berlin (Springer) 1993, 145--162. [Abstract]
  • Zur Abschätzung von Rechteck--Wahrscheinlichkeiten bei simultanen Tests (with H. Jäschke).
    Österreichische Zeitschrift für Statistik und Informatik (ZSI) 22 (1992), 219--242. [Abstract]
  • Some theory of stochastic dominance (with M. Scarsini).
    In: K. Mosler/M. Scarsini eds., Stochastic Orders and Decision under Risk, Hayward, California (Institute of Mathematical Statistics) 1991, 261--284. MR 94a:60024. [Full Paper as .PDF]
  • Multiattribute utility functions, partial information on coefficients, and efficient choice.
    OR Spektrum 13 (1991), 87--94. MR 92c:90027. [Full Paper as .PDF]
  • Location of physical distribution networks: A continuous approach.
    Locational Analysis 1 (1990), 189--202. [Abstract]
  • Estimation under G-invariant quasi-convex loss.
    Journal of Multivariate Analysis 22 (1987), 137--143. MR 88d:62091. [Full Paper as .PDF]
  • Simultane Konfidenzintervalle für die Mittelwerte nicht unabhängiger Zufallsgrössen.
    Allgemeines Statistisches Archiv 69 (1985), 377--391.
  • Minimax estimation of a multivariate location parameter under quasi-convex loss. Methods of Operations Research 55 (1985), 199-209.
  • Increasing multivariate risk: Some definitions.
    In: Risk and Capital, G. Bamberg/K. Spremann eds., Berlin (Springer) 1984, 88--102. MR 85h:90020. [Abstract]
  • Stochastic dominance decision rules when the attributes are utility independent.
    Management Science 30 (1984), 1311--1322. MR 86g:90005, Zbl. 554.90011. [Full Paper as .PDF]
  • Location theory of the firm facing uncertain prices and transport rates.
    In: Operations Research and Economic Theory, Essays in Honor of M. J. Beckmann. H. Hauptmann/W. Krelle/K. C. Mosler eds., Berlin (Springer) 1984, 163--174. Zbl. 542.90008.
  • Robust comparisons of spatial patterns.
    Regional Science and Urban Economics 14 (1984), 453--463. [Full Paper as .PDF]
  • Characterization of some stochastic orderings in multinormal and elliptic distributions.
    In: Operations Research Proceedings 1983, H. Steckhan et al. eds., Berlin (Springer) 1984, 520--527.\ MR 87g:90003, Zbl. 533.90011.
  • Assoziierte und positiv abhängige Zufallsvariable.
    Methods of Operations Research 44 (1981), 115--126.\ MR 84:90010, Zbl. 524.62056.
  • Halbordnungen zur Abschätzung des Verhaltens stochastischer Systeme.
    In: Anwendungen der Systemtheorie und Kybernetik in Wirtschaft und Verwaltung. H. Hauptmann/K. E. Schenk eds., Berlin (Duncker & Humblot) 1980, 179--192.
  • Statistical decisions between portfolios: Mean--variance analysis revisited.
    Engineering and Process Economics 4 (1979), 257--268. [Full Paper as .PDF]
  • Zur Dezentralisierung des quadratischen Standortproblems.
    Zeitschrift für die gesamte Staatswissenschaft 134 (1978), 464--476. [Full Paper as .PDF]
  • Minimum cost location of branched networks for transportation to a center.
    In: Advances in Operational Research. M. Roubens ed., Amsterdam (North--Holland) 1977, 311--329.\ Zbl. 372.90120.