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Multivariate dispersion orderings

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  • Giovagnoli, Alessandra
  • Wynn, H. P.

Abstract

A multivariate dispersion ordering is introduced in a weak and strong version. These arise naturally out of the consideration of two-sided versions of a well-known univariate dispersion ordering referred to as 'disp'. Various characterisations of the new orderings are given and some detailed results for the normal distribution. A final section points to applications.

Suggested Citation

  • Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:325-332
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    References listed on IDEAS

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    1. Eaton, Morris L. & Perlman, Michael D., 1991. "Concentration inequalities for multivariate distributions: I. multivariate normal distributions," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 487-504, December.
    2. Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
    3. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    4. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
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    1. Fernandez-Ponce, J. M. & Suarez-Llorens, A., 2003. "A multivariate dispersion ordering based on quantiles more widely separated," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 40-53, April.
    2. Alexander Zaigraev, 2002. "Shape optimal design criterion in linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 56(3), pages 259-273, December.
    3. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
    4. Ulysse Lawogni, 2019. "Measures of Inequality In Vectors Distributions," Working Papers hal-02377802, HAL.
    5. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    6. Alfred Galichon & Arthur Charpentier & Marc Henry, 2012. "Local Utility and Risk Aversion," Post-Print hal-03569250, HAL.
    7. Romanazzi, Mario, 2009. "Data depth, random simplices and multivariate dispersion," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1473-1479, June.
    8. Reza Modarres, 2020. "Graphical Comparison of High‐Dimensional Distributions," International Statistical Review, International Statistical Institute, vol. 88(3), pages 698-714, December.
    9. Guillermo Ayala & María Concepción López-Díaz & Miguel López-Díaz & Lucía Martínez-Costa, 2015. "Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 661-675, September.
    10. Carlos Carleos & Miguel López-Díaz, 2010. "A new family of dispersive orderings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 203-217, March.
    11. José Pablo Arias‐Nicolás & Félix Belzunce & Olga Núñez‐Barrera & Alfonso Suárez‐Llorens, 2009. "A multivariate IFR notion based on the multivariate dispersive ordering," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 339-358, May.
    12. María Concepción López-Díaz & Miguel López-Díaz & Sergio Martínez-Fernández, 2018. "Stochastic orders to approach investments in condor financial derivatives," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 122-146, March.
    13. Arthur Charpentier & Alfred Galichon & Marc Henry, 2016. "Local Utility and Multivariate Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 466-476, May.
    14. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.
    15. Volodina, Victoria & Wheatcroft, Edward & Wynn, Henry, 2022. "Comparing district heating options under uncertainty using stochastic ordering," LSE Research Online Documents on Economics 114292, London School of Economics and Political Science, LSE Library.
    16. Averous, Jean & Meste, Michel, 1997. "Median Balls: An Extension of the Interquantile Intervals to Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 222-241, November.
    17. repec:hal:spmain:info:hdl:2441/63913pp1o99dr9nneabam7071k is not listed on IDEAS
    18. Fernández-Ponce, J.M. & Rodríguez-Griñolo, R., 2006. "Preserving multivariate dispersion: An application to the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1208-1220, May.
    19. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    20. Ebrahimi, Nader & Kirmani, S.N.U.A. & Soofi, Ehsan S., 2007. "Multivariate dynamic information," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 328-349, February.
    21. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.
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