IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v26y2017i3d10.1007_s11749-017-0527-5.html
   My bibliography  Save this article

New properties of the orthant convex-type stochastic orders

Author

Listed:
  • J. M. Fernández-Ponce

    (Universidad de Sevilla)

  • M. R. Rodríguez-Griñolo

    (Universidad Pablo de Olavide)

Abstract

The orthant convex and concave orders have been studied in the literature as extensions of univariate variability orders. In this paper, new results are proposed for bivariate orthant convex-type orders between vectors. In particular, we prove that these orders cannot be considered as dependence orders since they fail to verify several desirable properties that any positive dependence order should satisfy. Among other results, the relationships between these orders under certain transformations are presented, as well as that the orthant convex orders between bivariate random vectors with the same means are sufficient conditions to order the corresponding covariances. We also show that establishing the upper orthant convex or lower orthant concave orders between two vectors in the same Fréchet class is not equivalent to establishing these orders between the corresponding copulas except when marginals are uniform distributions. Several examples related with concordance measures, such as Kendall’s tau and Spearman’s rho, are also given, as are results on mixture models.

Suggested Citation

  • J. M. Fernández-Ponce & M. R. Rodríguez-Griñolo, 2017. "New properties of the orthant convex-type stochastic orders," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 618-637, September.
  • Handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0527-5
    DOI: 10.1007/s11749-017-0527-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-017-0527-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11749-017-0527-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pellerey, Franco, 1999. "Stochastic Comparisons for Multivariate Shock Models," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 42-55, October.
    2. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    3. Eva María Ortega & José Alonso, 2014. "Recent issues on stochastic directional convexity, and new results on the analysis of systems for communication, information, time scales and maintenance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 479-496, July.
    4. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    5. Denuit, Michel & Mesfioui, Mhamed, 2016. "Multivariate Higher-Degree Stochastic Increasing Convexity," LIDAM Reprints ISBA 2016036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    7. Mulero, Julio & Pellerey, Franco & Rodríguez-Griñolo, Rosario, 2010. "Stochastic comparisons for time transformed exponential models," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 328-333, April.
    8. Denuit, Michel & Mesfioui, Mhamed, 2013. "A sufficient condition of crossing type for the bivariate orthant convex order," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 157-162.
    9. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Reprints ISBA 2010029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Agnieszka Goroncy & Tomasz Rychlik, 2015. "Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 175-204, February.
    11. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Discussion Papers ISBA 2010012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Denuit, Michel & Mesfioui, Mhamed, 2013. "A sufficient condition of crossing type for the bivariate orthant convex order," LIDAM Reprints ISBA 2013004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Mesfioui, Mhamed & Denuit, Michel M., 2015. "Comonotonicity, orthant convex order and sums of random variables," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 356-364.
    14. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
    15. Mesfioui, Mhamed & Denuit, Michel, 2015. "Comonotonicity, orthant convex order and sums of random variables," LIDAM Reprints ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michel M. Denuit & Mhamed Mesfioui, 2016. "Multivariate Higher-Degree Stochastic Increasing Convexity," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1599-1623, December.
    2. Denuit, Michel & Mesfioui, Mhamed, 2013. "Multivariate higher-degree stochastic increasing convexity," LIDAM Discussion Papers ISBA 2013016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Sordo, Miguel A., 2016. "A multivariate extension of the increasing convex order to compare risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 224-230.
    4. Mesfioui, Mhamed & Denuit, Michel M., 2015. "Comonotonicity, orthant convex order and sums of random variables," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 356-364.
    5. Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.
    6. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    7. Denuit, Michel M. & Mesfioui, Mhamed, 2017. "Preserving the Rothschild–Stiglitz type increase in risk with background risk: A characterization," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 1-5.
    8. Mesfioui, Mhamed & Denuit, Michel, 2014. "Comonotonicity, orthant convex order and sums of random variables," LIDAM Discussion Papers ISBA 2014002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.
    10. Li, Xiaohu & Lin, Jianhua, 2011. "Stochastic orders in time transformed exponential models with applications," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 47-52, July.
    11. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," LIDAM Discussion Papers ISBA 2019006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Haijun Li & Susan H. Xu, 2001. "Directionally Convex Comparison of Correlated First Passage Times," Methodology and Computing in Applied Probability, Springer, vol. 3(4), pages 365-378, December.
    13. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    14. Denuit, Michel & Mesfioui, Mhamed, 2012. "A sufficient condition of crossing-type for the bivariate orthant convex order," LIDAM Discussion Papers ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Denuit, Michel & Mesfioui, Mhamed, 2013. "A sufficient condition of crossing type for the bivariate orthant convex order," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 157-162.
    16. Denuit, Michel & Sznajder, Dominik & Trufin, Julien, 2019. "Model selection based on Lorenz and concentration curves, Gini indices and convex order," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 128-139.
    17. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    18. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    19. Bassan, Bruno & Denuit, Michel & Scarsini, Marco, 1999. "Variability orders and mean differences," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 121-130, November.
    20. Shaked, Moshe, 2007. "Stochastic comparisons of multivariate random sums in the Laplace transform order, with applications," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1339-1344, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0527-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.