Limit distributions of the minimax of independent identically distributed random variables
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- by Herman Chernoff and Henry Teicher
- Trans. Amer. Math. Soc. 116 (1965), 474-491
- DOI: https://doi.org/10.1090/S0002-9947-1965-0185640-3
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Abstract:
The class of limiting distributions of the normalized minimax (or maximin) of independent identically distributed random variables is obtained and the domains of attraction of the three limiting types are characterized. Asymptotic independence of the minimax and maximin is also demonstrated.References
- Herman Chernoff, Large-sample theory: parametric case, Ann. Math. Statist. 27 (1956), 1–22. MR 76245, DOI 10.1214/aoms/1177728347
- William Feller, An Introduction to Probability Theory and Its Applications. Vol. I, John Wiley & Sons, Inc., New York, N.Y., 1950. MR 0038583
- B. Gnedenko, Sur la distribution limite du terme maximum d’une série aléatoire, Ann. of Math. (2) 44 (1943), 423–453 (French). MR 8655, DOI 10.2307/1968974
- John W. Pratt, On a general concept of “in probability”, Ann. Math. Statist. 30 (1959), 549–558. MR 104283, DOI 10.1214/aoms/1177706267
Bibliographic Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 116 (1965), 474-491
- MSC: Primary 60.30
- DOI: https://doi.org/10.1090/S0002-9947-1965-0185640-3
- MathSciNet review: 0185640