Abstract
We propose a method for constructing statistical criteria. It can be used for testing an arbitrary finite set of simple alternative hypotheses. A concept of an optimal statistical criterion is introduced, special cases of which are the Bayesian criterion and the minimax criterion. It is proved that any optimal statistical criterion can be constructed on the basis of the likelihood ratio.
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Yu. V. Kuk and Yu. I. Petunin, “Optimal statistical criteria,”Dokl. Akad. Nauk Ukr. SSR, Ser A, No. 4, 298–300 (1976).
Yu. V. Kuk and Yu. I. Petunin, “Testing several hypotheses by using optimal statistical criteria,”Ukr. Mat. Zh. (to appear).
E. Lehmann,Testing Statistical Hypotheses [Russian translation], Nauka, Moscow (1964).
Sh. Zacks,The Theory of Statistical Inference, Wiley, New York (1971).
S. G. Krein and Yu. I. Petunin, “Scales for Banach spaces,”Usp. Mat. Nauk.,21, Issue 2, 89–168 (1966).
B. N. Pshenichnyi,Necessary Conditions of Extremum [in Russian], Nauka, Moscow (1969).
M. De Groot,Optimal Statistical Decisions [Russian translation], Mir, Moscow (1974).
C. R. Rao and P. Slater, “Multivariate analysis applied to differences between neurotic groups,”Brit. J. Psychol. (Statist. Sec.),2, No. 1, 17–26 (1949).
D. Middleton,Introduction into Statistical Communication Theory [Russian translation], Sov. Radio, Moscow (1962).
M. Kendall and A. Stuart,The Advanced Theory of Statistics, Vol. 3: Design and Analysis, and Time-Series, Wiley, New York (1974).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 378–388, April, 1994.
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Kuk, Y.V., Petunin, Y.I. Testing hypotheses by using optimal statistical criteria. I. Ukr Math J 46, 396–407 (1994). https://doi.org/10.1007/BF01060409
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DOI: https://doi.org/10.1007/BF01060409