Geodesic
Asymptotic expansion of the coverage probability of James--Stein estimators
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 4, pp. 776-785

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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, multivariate normal distribution, coverage probability, asymptotic expansion.
Mots-clés : Stein estimation 
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     title = {Asymptotic expansion of the coverage probability of {James--Stein} estimators},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_4_a7/}
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E. S. Ahmed; A. K. Md. E. Saleh; A. I. Volodin; I. N. Volodin. Asymptotic expansion of the coverage probability of James--Stein estimators. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 4, pp. 776-785. http://geodesic.mathdoc.fr/item/TVP_2006_51_4_a7/