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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 4, Pages 776–785 (Mi tvp25)  

This article is cited in 8 scientific papers (total in 8 papers)

Short Communications

Asymptotic expansion of the coverage probability of James–Stein estimators

E. S. Ahmeda, A. K. Md. E. Salehb, A. I. Volodinc, I. N. Volodind

a University of Windsor
b Carleton University
c University of Regina
d Kazan State University

Abstract: This paper provides a new approach to the asymptotic expansion construction of the coverage probability of the confidence sets recentered in [W. James and C. Stein, Estimation with quadratic loss, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, Univ. California Press, Berkeley, CA, 1961, pp. 361–379] and its positive-part Stein estimators [C. Stein, J. Roy. Statist. Soc. Ser. B, 24 (1962), pp. 265–296]. The coverage probability of these confidence sets depends on the noncentrality parameter $\tau^2$ as in the case of risks of these estimators. The new approach (which is different than Berger's [J. O. Berger, Ann. Statist., 8 (1980), pp. 716–761] and Hwang and Casella's [J. T. Hwang and G. Casella, Statist. Decisions, suppl. 1 (1984), pp. 3–16]) allows us to obtain the asymptotics analysis of the coverage probabilities for the two cases, namely, when $\tau^2\to 0$ and $\tau^2\to\infty$. For both cases we provide a simple approximation of the coverage probabilities. Some graphical and tabular results are provided to assess the accuracy of our approximations.

Keywords: confidence sets, James–Stein estimators, Stein estimation, multivariate normal distribution, coverage probability, asymptotic expansion.


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English version:
Theory of Probability and its Applications, 2007, 51:4, 683–695

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Received: 17.11.2004

Citation: E. S. Ahmed, A. K. Md. E. Saleh, A. I. Volodin, I. N. Volodin, “Asymptotic expansion of the coverage probability of James–Stein estimators”, Teor. Veroyatnost. i Primenen., 51:4 (2006), 776–785; Theory Probab. Appl., 51:4 (2007), 683–695

Citation in format AMSBIB
\by E.~S.~Ahmed, A.~K.~Md.~E.~Saleh, A.~I.~Volodin, I.~N.~Volodin
\paper Asymptotic expansion of the coverage probability of James--Stein estimators
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 4
\pages 776--785
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 4
\pages 683--695

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    This publication is cited in the following articles:
    1. Ahmed S.E., Volodin A.I., Volodin I.N., “High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator”, Statist. Probab. Lett., 79:17 (2009), 1823–1828  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ejaz Ahmed S., Liu Shuangzhe, “Asymptotic theory of simultaneous estimation of Poisson means”, Linear Algebra Appl., 430:10 (2009), 2734–2748  crossref  mathscinet  zmath  isi  scopus
    3. I. N. Volodin, I. A. Kareev, “Doveritelnye mnozhestva Dzheimsa–Steina: metod ravnykh ploschadei pri globalnoi approksimatsii veroyatnosti nakrytiya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 152, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2010, 132–141  mathnet  mathscinet
    4. Raheem S.M.E., Ahmed S.E., Doksum K.A., “Absolute penalty and shrinkage estimation in partially linear models”, Computational Statistics & Data Analysis, 56:4 (2012), 874–891  crossref  mathscinet  zmath  isi  scopus
    5. Ahmed S.E., Muttlak H.A., Al-Mutawa J., Saheh M., “Stein-Type Estimation Using Ranked Set Sampling”, J. Stat. Comput. Simul., 82:10 (2012), 1501–1516  crossref  mathscinet  zmath  isi  elib  scopus
    6. Ahmed S.E., Kareev I., Suraphee S., Volodin A., Volodin I., “Confidence Sets Based on the Positive Part James-Stein Estimator With the Asymptotically Constant Coverage Probability”, J. Stat. Comput. Simul., 85:12 (2015), 2506–2513  crossref  mathscinet  isi  elib  scopus
    7. Wei B., Lee S.M.S., Wu X., “Stochastically optimal bootstrap sample size for shrinkage-type statistics”, Stat. Comput., 26:1-2 (2016), 249–262  crossref  mathscinet  zmath  isi  elib  scopus
    8. Suraphee S., Viriyapong N., Chutiman N., Chiangpradit M., “The Third Order Approximation For the Coverage Probability of a Confidence Set Centered At the Positive Part James-Stein Estimator”, Thail. Statist., 16:2 (2018), 94–105  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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