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High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator

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  • Ahmed, S. Ejaz
  • Volodin, Andrei I.
  • Volodin, Igor N.

Abstract

In this paper we continue our investigation connected with the new approach developed in Ahmed et al. [Ahmed, S.E., Saleh, A.K.Md.E., Volodin, A., Volodin, I., 2006. Asymptotic expansion of the coverage probability of James-Stein estimators. Theory Probab. Appl. 51 (4) 1-14] for asymptotic expansion construction of coverage probabilities, for confidence sets centered at James-Stein and positive-part James-Stein estimators. The coverage probabilities for these confidence sets depend on the noncentrality parameter [tau]2, the same as the risks of these estimators. In this paper we consider only the confidence set centered at the positive-part James-Stein estimator. As is shown in the above-mentioned reference, the new approach provides a method to obtain for the given confidence set, an asymptotic expansion of the coverage probability as one formula for both cases [tau]-->0 and [tau]-->[infinity]. We obtain the third terms of the asymptotic expansion for both mentioned cases, that is, the coefficients at [tau]2 and [tau]-2. Numerical illustrations show that the third term has only a small influence on the accuracy of the asymptotic estimation of coverage probability.

Suggested Citation

  • Ahmed, S. Ejaz & Volodin, Andrei I. & Volodin, Igor N., 2009. "High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1823-1828, September.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:17:p:1823-1828
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    References listed on IDEAS

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    1. Bradley Efron, 2006. "Minimum volume confidence regions for a multivariate normal mean vector," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 655-670, September.
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    Cited by:

    1. Nkurunziza, Sévérien, 2011. "Shrinkage strategy in stratified random sample subject to measurement error," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 317-325, February.
    2. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
    3. Ejaz Ahmed, S. & Fallahpour, Saber, 2012. "Shrinkage estimation strategy in quasi-likelihood models," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2170-2179.
    4. Ahmed, S. Ejaz & Hussein, Abdulkadir & Nkurunziza, Sévérien, 2010. "Robust inference strategy in the presence of measurement error," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 726-732, April.

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