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Global Dependence Stochastic Orders

Author

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  • Moshe Shaked

    (University of Arizona)

  • Miguel A. Sordo

    (Universidad de Cádiz)

  • Alfonso Suárez-Llorens

    (Universidad de Cádiz)

Abstract

Two basic ideas, that give rise to global dependence stochastic orders, are introduced and studied. The similarities and differences between the resulting global dependence orders, and the known common positive dependence orders, are discussed. Some desirable properties that global dependence orders may expected to satisfy are listed and checked. Three particular global dependence orders, that come up from the two general ideas, are studied in detail. It is shown, among other things, how these orders can be verified. Finally, some applications in auction theory, in reliability theory, and in economics, are described.

Suggested Citation

  • Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9253-8
    DOI: 10.1007/s11009-011-9253-8
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    References listed on IDEAS

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    1. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.
    2. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
    3. Takemi Yanagimoto & Masashi Okamoto, 1969. "Partial orderings of permutations and monotonicity of a rank correlation statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 489-506, December.
    4. Z. Fang & H. Joe, 1992. "Further developments on some dependence orderings for continuous bivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 501-517, September.
    5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    6. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    8. Shlomo Yitzhaki & Edna Schechtman, 2005. "The properties of the extended Gini measures of variability and inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 401-433.
    9. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    10. 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.
    11. Denuit, Michel, 2010. "Positive dependence of signals," LIDAM Discussion Papers ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
    13. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    14. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    15. Juan-JosÈ Ganuza & JosÈ S. Penalva, 2010. "Signal Orderings Based on Dispersion and the Supply of Private Information in Auctions," Econometrica, Econometric Society, vol. 78(3), pages 1007-1030, May.
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    Cited by:

    1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
    2. Alessandro Arlotto & J. Michael Steele, 2018. "A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 839-854, September.
    3. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Brandt, Nikolai & Drees, Burkhard & Eckwert, Bernhard & Várdy, Felix, 2014. "Information and the dispersion of posterior expectations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 604-611.
    5. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 485-497.
    6. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    7. Denuit, Michel & Robert, Christian Y., 2020. "From risk sharing to risk transfer: the analytics of collaborative insurance," LIDAM Discussion Papers ISBA 2020017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Michel Denuit & Mhamed Mesfioui & Julien Trufin, 2019. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 491-509, June.

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