Summary
Inequalities for the rearrangement of functions are applied to obtain a solution of a statistical optimization problem. This optimization problem arises in situations where one wants to describe the influence of stochastic dependence on a statistical problem.
Similar content being viewed by others
References
Chong, K.-M.: Some extensions of a theorem of Hardy, Littlewood and Polya and their applications. Canad. J. Math.26, 1974, 1321–1340.
Chong, K.-M., andN.M. Rice: Equimeasurable rearrangement of functions. Queen's Papers in Pure and Applied Mathematics28, 1971.
Dall'Aglio, G.: Fréchet classes and compatibility of distribution functions. Symposia Mathematica9, 1972, 131–150.
Day, P.W.: Rearrangement inequalities. Canad. J. Math.24, 1972, 930–943.
Gaffke, N., andL. Rüschendorf: On a class of extremal problems in statistics. Mathem. Operationsforschung und Statistik. Series Optimization12, 1981, 123–136.
Hardy, G.H., J.E. Littlewood andG. Polya: Inequalities. 2nd ed. Cambridge 1952.
Ky Fan, andG.G. Lorentz: An integral inequality. Amer. Math. Monthly61, 1954, 626–631.
Lorentz, G.G.: An inequality for rearrangements. Amer. Math. Monthly60, 1953, 176–179.
Luxemburg, W.A.J.: Rearrangement invariant Banach function spaces. Queen's Papers in Pure and Applied Mathematics10, 1967, 83–144.
Marshall, A.W., andI. Olkin: Inequalities: Theory of Majorization and Its Applications. New York 1979.
Parthasaraty, K.R.: Probability Measures on Metric Spaces. New York 1967.
Rohlin, V.A.: On the Fundamental Ideas of Measure Theory. Amer. Math. Soc. Transl.71, 1952.
Rüschendorf, L.: Sharpness of Fréchet-bounds. Z. Wahrscheinlichkeitstheorie verw. Gebiete57, 1981, 293–302.
Ryff, J.V.: Orbits ofL 1 functions under doubly stochastic transformations. Trans. Amer. Math. Soc.117, 1965, 92–100.
Schaefer, M.: Notes on thek-dimensional Jensen inequality. Ann. Prob.4, 1976, 502–504.
Stoyan, D.: Halbordnungsrelationen für Verteilungsgesetze. Math. Nachr.52, 1972, 315–331.
Stoyan, D.: Qualitative Eigenschaften und Abschätzungen stochastischer Modelle. München 1977.
Whitt, M.: Bivariate distributions with given marginals. Ann. Statist.4, 1976, 1280–1289.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rüschendorf, L. Solution of a statistical optimization problem by rearrangement methods. Metrika 30, 55–61 (1983). https://doi.org/10.1007/BF02056901
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02056901