zbMATH — the first resource for mathematics

On the uniform almost sure convergence of losses for the repetition of a statistical decision problem. (English) Zbl 0204.51703

Full Text: EuDML
[1] C. G. Esseen: On the Kolmogorov-Rogozin Inequality for the Concentration Function. Z. Wahrscheinlichkeitstheorie und Verw. Geb. 5 (1966), 210-216. · Zbl 0142.14702
[2] P. R. Halmos: Measure Theory. New York 1950. · Zbl 0040.16802
[3] J. Hannan: Approximation to Bayes Risk in Repeated Play. Contributions to the Theory of Games 3, 97-139. , · Zbl 0078.32804
[4] S. Jílovec B. Šubert: Repetitive Play of a Game against Nature. Aplikace matematiky 12 (1967), 383-397.
[5] S. Jílovec: Последовательное повторение игры при неопределености. Kybernetika 3 (1967), 560-586.
[6] S. Jílovec: Равномерная сходомость потерь в небайесовской модели статистического решения. Research report. ÚTIA-ČSAV, 1967.
[7] S. Jílovec: O vlastnostech jednoho strategického postupu při opakovaném rozhodování. Research repor. ÚTIA-ČSAV, 1969.
[8] M. Loève: Probability Theory. New York 1963.
[9] E. Parzen: On Uniform Convergence of Families of Sequences of Random Variables. Univ. of California Publ. in Statist. 2 (1954), 23-54. · Zbl 0059.12303
[10] E. Samuel: Asymptotic Solutions of the Sequential Compound Decision Problem. Ann. Math. Statist. 34 (1963), 1079-1094. · Zbl 0202.49102
[11] E. Samuel: Convergence of the Losses of Certain Decision Rules for the Sequential Compound Decision Problem. Ann. Math. Statist. 35 (1964), 1606-1621. · Zbl 0134.35903
[12] B. Šubert: An Asymptotically Optimal Decision Procedure. Transaction of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Prague 1967, 573-587.
[13] B. Šubert: Repetitive Play of an Unknown Game Against Nature. Stanford University Report No. 6151-6153, December 1967.
[14] J. Van Ryzin: The Sequential Compound Decision Problem with \(m \times n\) Finite Loss Matrix. Ann. Math. Statist. 37 (1966), 954-975. · Zbl 0173.46303
[15] J. Van Ryzin: Repetitive Play in Finite Statistical Games with Unknown Distributions. Ann. Math. Statist. 37 (1966), 976-994. · Zbl 0173.47802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.