Abstract
In this work, we define objective and subjective consistent criteria for hypotheses testing. Sufficient conditions for the existence of such criteria are given in the case of Borel probability measures. At the same time, we construct the subjective consistent criterion for hypotheses testing, as well as the statistical structure, which admits the objective consistent criterion for hypotheses testing.
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Notes
- 1.
We call a finite-dimensional subspace \(P\subset V\) a probe for a set \(T\subset V\) if Lebesgue measure supported on P is transverse to a Borel set which contains the complement of T (see Definition 6 from [4]).
References
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Purtukhia, O., Zerakidze, Z. (2020). Objective and Subjective Consistent Criteria for Hypotheses Testing. In: Jaiani, G., Natroshvili, D. (eds) Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol 334. Springer, Cham. https://doi.org/10.1007/978-3-030-56356-1_14
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DOI: https://doi.org/10.1007/978-3-030-56356-1_14
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