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Parametric Statistical Inference in the Zone of Moderate ...
[Submitted on 27 Apr 2026 (v1), last revised 16 Aug 2026 (this v · 2026-04-28 · via stat updates on arXiv.org

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Abstract:A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger distance. The Large Deviation Principle in the moderate deviation probability zone is proven for Bayesian estimators and maximum likelihood estimators. A uniform approximation of the logarithm of the likelihood ratio and Theorem on concentration of the posterior Bayesian measure are also established for the zone of moderate deviation probabilities.

Submission history

From: Mikhail Ermakov s [view email]
[v1] Mon, 27 Apr 2026 17:42:35 UTC (16 KB)
[v2] Sun, 16 Aug 2026 18:58:27 UTC (16 KB)