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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 4, Pages 676–700
DOI: https://doi.org/10.4213/tvp251
(Mi tvp251)
 

This article is cited in 11 scientific papers (total in 11 papers)

On asymptotically efficient statistical inference for moderate deviation probabilities

M. S. Ermakov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
References:
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.
Received: 23.12.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 4, Pages 622–641
DOI: https://doi.org/10.1137/S0040585X97980701
Bibliographic databases:
Language: Russian
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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\by M.~S.~Ermakov
\paper On asymptotically efficient statistical inference for moderate
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\jour Teor. Veroyatnost. i Primenen.
\yr 2003
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\issue 4
\pages 676--700
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\zmath{https://zbmath.org/?q=an:1054.62015}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 4
\pages 622--641
\crossref{https://doi.org/10.1137/S0040585X97980701}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000226305500004}
Linking options:
  • https://www.mathnet.ru/eng/tvp251
  • https://doi.org/10.4213/tvp251
  • https://www.mathnet.ru/eng/tvp/v48/i4/p676
  • This publication is cited in the following 11 articles:
    1. Theory Probab. Appl., 69:1 (2024), 150–160  mathnet  crossref  crossref
    2. M. S. Ermakov, “Lokalnaya asimptoticheskaya normalnost logarifma otnosheniya pravdopodobiya v zone veroyatnostei umerennykh uklonenii”, Veroyatnost i statistika. 34, Posvyaschaetsya yubileyu Andreya Nikolaevicha BORODINA, Zap. nauchn. sem. POMI, 525, POMI, SPb., 2023, 71–85  mathnet
    3. Cmiel B. Inglot T. Ledwina T., “Intermediate Efficiency of Some Weighted Goodness-of-Fit Statistics”, J. Nonparametr. Stat., 32:3 (2020), 667–703  crossref  mathscinet  isi
    4. Inglot T., “Intermediate Efficiency of Tests Under Heavy-Tailed Alternatives”, Prob. Math. Stat.., 40:2 (2020), 331–348  crossref  mathscinet  isi
    5. Inglot T. Ledwina T. Cmiel B., “Intermediate Efficiency in Nonparametric Testing Problems With An Application to Some Weighted Statistics”, ESAIM-Prob. Stat., 23 (2019), 697–738  crossref  mathscinet  isi
    6. 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
    7. M. S. Ermakov, “On asymptotically efficient statistical inference on a signal parameter”, J. Math. Sci. (N. Y.), 206:2 (2015), 159–170  mathnet  crossref
    8. 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
    9. Mikhail Ermakov, “Nonparametric signal detection with small type I and type II error probabilities”, Stat Inference Stoch Process, 14:1 (2011), 1  crossref
    10. 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
    11. M. S. Ermakov, “On semiparametric inference in moderate deviation zone”, J. Math. Sci. (N. Y.), 152:6 (2008), 869–874  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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