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.
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Volume (Year): 79 (2009) Issue (Month): 17 (September) Pages: 1823-1828 Download reference. The following formats are available: HTML
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