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Original Articles

Confidence sets based on the positive part James–Stein estimator with the asymptotically constant coverage probability

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Pages 2506-2513 | Received 01 Dec 2013, Accepted 06 Jun 2014, Published online: 15 Jul 2014

References

  • Stein C. Inadmissibility of the usual estimator for the mean of a multivariate distribution. Proc Third Berkeley Symp Math Statist Prob. 1956;1:197–206.
  • Stein C. Confidence sets for the mean of a multivariate normal distribution. J R Stat Soc Ser B. 1962;24:265–296.
  • James W, Stein C. Estimation with quadratic loss. Proc Fourth Berkeley Symp Math Statist Probab. 1961;1:361–380.
  • Tsukuma H, Kubokawa T. Methods for improved in estimation of a normal mean matrix. J Multivariate Anal. 2007;98:1592–1610. doi: 10.1016/j.jmva.2007.04.009
  • Eldar YC, Chernoi JS. A pre-test like estimator dominating the least-squares method. J Statist Plann Inference. 2008;138:3069–3085. doi: 10.1016/j.jspi.2007.12.002
  • Hartung J, Knapp G, Sinha BK. Statistical meta-analysis with applications. Hoboken, NJ: John Wiley & Sons; 2011.
  • Ahmed SE, Saleh AK, Volodin AI, Volodin IN. Asymptotic expansion of the coverage probability of James-Stein estimators. Theory Probab Appl. 2007;51:683–695. doi: 10.1137/S0040585X97982712
  • Ahmed SE, Volodin AI, Volodin IN. High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator. Statist Probab Lett. 2009;79:1823–1828. doi: 10.1016/j.spl.2009.05.009
  • Kazimi C, Brownstone D. Bootstrap confidence bands for shrinkage estimators. J Econometrics. 1999;90:99–127. doi: 10.1016/S0304-4076(98)00037-2
  • Lehmann EL, Casella G. Theory of point estimation. 2nd ed. New York: Springer-Verlag; 1998.
  • Hwang JT, Casella G. Minimax confidence sets for the mean of a multivariate normal distribution. Ann Statist. 1982;10:868–881. doi: 10.1214/aos/1176345877

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