Summary
Under reasonable conditions on Θ, both errors of the tests that the law of a sample of size n belongs to Θ, go to zero like exp[−αn] and exp[− βn]. We shall determine the best possible values for α and β and give a construction of sequences of tests for which the errors decrease with such an optimal rate.
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Je tiens à remercier tout particulièrement G. Tusnády pour de nombreuses et très utiles suggestions et critiques concernant une première version de cet article.
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Birgé, L. Vitesses maximales de décroissance des erreurs et tests optimaux associés. Z. Wahrscheinlichkeitstheorie verw Gebiete 55, 261–273 (1981). https://doi.org/10.1007/BF00532119
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DOI: https://doi.org/10.1007/BF00532119