TY - JOUR

T1 - High order approximation for the coverage probability by a confident set centered at the positive-part James-Stein estimator

AU - Ejaz Ahmed, S.

AU - Volodin, Andrei

AU - Volodin, I.N.

PY - 2009

Y1 - 2009

N2 - 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 τ2, 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 τ→0 and τ→∞. We obtain the third terms of the asymptotic expansion for both mentioned cases, that is, the coefficients at τ2 and τ−2. Numerical illustrations show that the third term has only a small influence on the accuracy of the asymptotic estimation of coverage probability.

AB - 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 τ2, 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 τ→0 and τ→∞. We obtain the third terms of the asymptotic expansion for both mentioned cases, that is, the coefficients at τ2 and τ−2. Numerical illustrations show that the third term has only a small influence on the accuracy of the asymptotic estimation of coverage probability.

U2 - 10.1016/j.spl.2009.05.009

DO - 10.1016/j.spl.2009.05.009

M3 - Article

VL - 79

SP - 1823

EP - 1828

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

IS - 17

ER -