Geodesic
James–Stein confidence sets: equal area approach in the global approximation for the coverage probability
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 132-141 Cet article a éte moissonné depuis la source Math-Net.Ru

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In paper [Ahmed S. E., Saleh A. K. MD. E., Volodin A. I., Volodin I. N. Asymptotic expansion of the coverage probability of James–Stein estimators // Theory Probab. Appl. – 2007. – V. 51. – P. 683–695] an asymptotic expansion of the coverage probabilities for the James–Stein confidence sets was constructed, which is accurate both for large and small values of the noncentrality parameter $\tau^2$ – the sum of the squares of the means of $p\geq3$ normal distributions. As numerical illustrations show, the expansion might be used almost in the entire area of the values of $\tau^2$ with the error of the order $10^{-2}$. In the present article a similar asymptotic expansion is suggested, whose global error is significantly less in the area of small and moderate values of $p$. The accuracy of the obtained results is shown by the Monte-Carlo statistical simulations.
Keywords: confidence sets, positive-part James–Stein estimator, multivariate normal distribution, coverage probability, asymptotic expansion. 
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I. N. Volodin; I. A. Kareev. James–Stein confidence sets: equal area approach in the global approximation for the coverage probability. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 132-141. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a12/

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