Geodesic
Optimal substitution of arguments of an arrangement increasing function based on sufficient statistics for parameters-arguments
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 185-211 
M. I. Revyakov. Optimal substitution of arguments of an arrangement increasing function based on sufficient statistics for parameters-arguments. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 185-211. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a9/
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     author = {M. I. Revyakov},
     title = {Optimal substitution of arguments of an arrangement increasing function based on sufficient statistics for parameters-arguments},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {185--211},
     year = {2010},
     volume = {384},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The aim of this paper is to find the conditions under which optimal permutation of arguments of (goal) multivariate arrangement increasing functions of parameters of distributions must be realised, according to the same rule as if parameters-arguments ordering being the same as ordering of corresponding sufficient statistics. Those results are used in the maximization problems of reliability of systems based on the test results of their components. Bibl. 16 titles.

[1] R. E. Bechhofer, J. Kiefer, M. Sobel, Sequential Identification and Ranking Procedures, Univ. Chicago Press, 1968 | MR | Zbl

[2] P. J. Boland, F. Proschan, “Multivariate arrangement increasing functions with applications in probability and statistics”, J. Multivariate Anal., 25 (1988), 286–298 | DOI | MR | Zbl

[3] P. J. Boland, F. Proschan, Y. L. Tong, “Optimal arrangement of components via pairwise rearrangement”, Nav. Res. Logist., 36 (1989), 807–815 | 3.0.CO;2-I class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[4] D. J. Devis, “An analysis of some failure data”, J. Amer. Statist. Assoc., 47 (1952), 113–150 | DOI

[5] J. T. Hwang, “Universal domination and stochastic domination: estimator simultaneously under a broad class of loss functions”, Ann. Statist., 13:1 (1985), 295–314 | DOI | MR | Zbl

[6] L. B. Klebanov, “ ‘Universalnye’ funktsii poter i nesmeschennye otsenki”, Dokl. AN SSSR, 20:6 (1972), 1249–1251 | MR

[7] E. L. Lehmann, “On a theorem of Bahadur and Goodman”, Ann. Math. Statist., 37 (1966), 1–6 | DOI | MR | Zbl

[8] E. Leman, Proverka statisticheskikh gipotez, Fizmatgiz, M., 1979 | MR

[9] A. Marshall, I. Olkin, Neravenstva: Teoriya mazhorizatsii i ee prilozheniya, Mir, M., 1983 | MR | Zbl

[10] G. Pledger, F. Proschan, “Comparisons of order statistics and of spacings from heterogeneous distributions”, Optimizing Methods in Statistics, ed. J. S. Rustagi, Academic Press, New York, 1971, 89–113 | DOI | MR

[11] F. Proschan, J. Sethuraman, “Stochastic comparison of order statistics from heterogeneous populations, with applications in reliability”, J. Multivariate Anal., 6 (1976), 608–616 | DOI | MR | Zbl

[12] M. I. Revyakov, “Ranking of populations in parameter`s modulus”, Statistics and Decisions, 21 (2003), 185–195 | DOI | MR | Zbl

[13] M. I. Revyakov, “Component allocation for a distributed system: reliability maximization”, J. Appl. Prob., 30:2 (1993), 471–477 | DOI | MR | Zbl

[14] T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach, Academic Press, 1967 | MR | Zbl

[15] R. Barlou, F. Proshan, Statisticheskaya teoriya nadezhnosti i ispytaniya na bezotkaznost, Nauka, M., 1984 | MR

[16] M. L. Eaton, “Some optimum properties of ranking procedures”, Ann. Math. Statist., 38 (1967), 124–137 | DOI | MR | Zbl