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Schur-convexity of 2nd order, certain subclass of multivariate arrangement increasing functions with applications in statistics

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  • Revyakov, Mikhail

Abstract

It is shown that starting with a certain meaningful problem of the type “ranking of populations”, a need arises to employ functions which we call “Schur-convex of 2nd order with respect to two variables”. These functions L(v1,v2,v3,…,vn) are symmetric, and they are characterized in essence by the relation Lv12″−2Lv1v2″+Lv22″≥0. It is shown that this subclass of Schur-convex functions is closely related to a certain subclass of multivariate arrangement increasing functions introduced by Boland and Proschan [P.J. Boland, F. Proschan, Multivariate arrangement increasing functions with applications in probability and statistics, J. Multivariate Anal. (1988) 25 286–298]. This relation allows us to solve a series of statistical problems concerning maximization of the goal function with respect to the risk criterion on the set of permutations of the function’s arguments.

Suggested Citation

  • Revyakov, Mikhail, 2013. "Schur-convexity of 2nd order, certain subclass of multivariate arrangement increasing functions with applications in statistics," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 25-34.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:25-34
    DOI: 10.1016/j.jmva.2012.11.013
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    References listed on IDEAS

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    1. Revyakov Mikhail, 2003. "Ranking of populations in parameter′s modulus," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 185-195, February.
    2. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May.
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