Abstract
The minimax hypothesis-testing problem is considered. Let H0: f=f0≡1 and H1 consist of smooth densities. It is shown that the optimal, in the minimax sense, order of distinguishing is attained by a procedure based on simultaneous use ofχ 2-tests corresponding to the growing number of intervals of grouping of the sample. Bibliography: 16 titles.
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 150–166.
Translated by S. Yu. Pilyugin.
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Ingster, Y.I. Adaptive chi-square tests. J Math Sci 99, 1110–1119 (2000). https://doi.org/10.1007/BF02673632
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DOI: https://doi.org/10.1007/BF02673632