Probabilities of moderate deviations

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1982 English Publisher:Springer Science and Business Media LLCJournal:Journal of Soviet Mathematics, volume 20, pages 2,123-2,130 (issn: 0090-4104, eissn: 1573-8795,

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Authors: Amosova, N. N.;

doi: 10.1007/bf01239988

Probabilities of moderate deviations

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Abstract

Let X1, X2, ... be a sequence of independent, identically distributed random variables, and let . The rate of convergence of probabilities of the form and is studied for any ɛ > ɛ0 and some r and ɛ0. Moreover, necessary and sufficient conditions are given that the relations be satisfied uniformly with respect to x in the region 0 ≤ x ≤ c√log n, where σ and c are some positive constants, and . Local limit theorems are also presented.

Keywords

Large deviations, probabilities of moderate deviations, Central limit and other weak theorems, rate of convergence

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