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Generalization of discrimination-rate theorems of Chernoff and Stein. (English) Zbl 0727.62026
The author considers a simple hypothesis and alternative about an abstract parametrized random observation from a directed set. The asymptotics over this set are evaluated for mixed errors of the Bayes test and second kind errors of the Neyman-Pearson tests.
By using simple properties of Rényi distances established by F. Liese and the author [Convex statistical distances. (1987; Zbl 0656.62004)], and from elementary inequalities established for Rényi distances by O. Krafft and D. Plachky [Ann. Math. Stat. 41, 1646-1654 (1970; Zbl 0214.180)] and the author [Studia Sci. Math. Hungar. 6(1971), 317-333 (1972; Zbl 0243.62034)], he shows that extensions to the observations consisting of segments of random sequences, processes and fields, essentially depend on the existence of an asymptotic Rényi distance of the hypothesis and alternative. This distance describes the discrimination rates attained by Bayes and Neyman- Pearson tests.

MSC:
 62F03 Parametric hypothesis testing 62F15 Bayesian inference 62B10 Statistical aspects of information-theoretic topics 62B99 Sufficiency and information 62F05 Asymptotic properties of parametric tests
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