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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 4, Pages 676–700 (Mi tvp251)  

This article is cited in 5 scientific papers (total in 5 papers)

On asymptotically efficient statistical inference for moderate deviation probabilities

M. S. Ermakov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We study the lower bounds of efficiency for the moderate deviation probabilities of tests and estimators. These bounds cover both the logarithmic and strong asymptotics. For the problems of hypothesis testing we propose a natural representation for the lower bounds of type I and type II error probabilities in terms of inverse function of the standard normal distribution. The lower bounds for the moderate deviation probabilities of estimators are deduced easily from the corresponding bounds in hypothesis testing.

Keywords: large deviations, moderate deviations, efficiency, Bahadur efficiency, Chernoff efficiency.

DOI: https://doi.org/10.4213/tvp251

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English version:
Theory of Probability and its Applications, 2004, 48:4, 622–641

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Received: 23.12.2002

Citation: M. S. Ermakov, “On asymptotically efficient statistical inference for moderate deviation probabilities”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 676–700; Theory Probab. Appl., 48:4 (2004), 622–641

Citation in format AMSBIB
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\paper On asymptotically efficient statistical inference for moderate
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\jour Teor. Veroyatnost. i Primenen.
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\issue 4
\pages 676--700
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 4
\pages 622--641
\crossref{https://doi.org/10.1137/S0040585X97980701}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000226305500004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. S. Ermakov, “On semiparametric inference in moderate deviation zone”, J. Math. Sci. (N. Y.), 152:6 (2008), 869–874  mathnet  crossref
    2. M. S. Ermakov, “Nonparametric Hypothesis Testing with Small Type I or Type II Error Probabilities”, Problems Inform. Transmission, 44:2 (2008), 119–137  mathnet  crossref  mathscinet  isi
    3. Ermakov M., “The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation Probabilities”, Electron. J. Stat., 6 (2012), 2150–2184  crossref  mathscinet  zmath  isi  elib  scopus
    4. M. S. Ermakov, “On asymptotically efficient statistical inference on a signal parameter”, J. Math. Sci. (N. Y.), 206:2 (2015), 159–170  mathnet  crossref
    5. Ji P. Nussbaum M., “Sharp Minimax Adaptation Over Sobolev Ellipsoids in Nonparametric Testing”, Electron. J. Stat., 11:2 (2017), 4515–4562  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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