Ghosh, Malay; Kim, Dal Ho; Kim, Myung Joon Asymptotic mean squared error of constrained James-Stein estimators. (English) Zbl 1091.62008 J. Stat. Plann. Inference 126, No. 1, 107-118 (2004). Summary: We consider the asymptotic expansion of the MSE of constrained James–Stein estimators. We provide an estimator of the MSE which is asymptotically valid up to \(O(m^{-1})\). A simulation study is undertaken to evaluate the performance of these estimators. Cited in 1 Document MSC: 62F12 Asymptotic properties of parametric estimators 62E20 Asymptotic distribution theory in statistics Keywords:Constrained empirical Bayes; Mean squared error; Asymptotics PDFBibTeX XMLCite \textit{M. Ghosh} et al., J. Stat. Plann. Inference 126, No. 1, 107--118 (2004; Zbl 1091.62008) Full Text: DOI References: [1] Datta, G. S.; Lahiri, P., A unified measure of uncertainty of estimated best linear unbiased predictors in small-area estimation problems, Statist. Sinica, 10, 613-628 (2000) · Zbl 1054.62566 [2] Efron, B.; Morris, C., Stein’s estimation rule and its competitors—an empirical Bayes approach, J. Amer. Statist. Assoc., 68, 117-130 (1973) · Zbl 0275.62005 [3] Ghosh, M., Constrained Bayes estimation with applications, J. Amer. Statist. Assoc., 87, 533-540 (1992) · Zbl 0781.62040 [4] James, W., Stein, C., 1961. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical and Statistical Problems, Vol. 1. University of California Press, Berkeley, pp. 361-380.; James, W., Stein, C., 1961. Estimation with quadratic loss. Proceedings of the Fourth Berkeley Symposium on Mathematical and Statistical Problems, Vol. 1. University of California Press, Berkeley, pp. 361-380. · Zbl 1281.62026 [5] Lahiri, P.; Rao, J. N.K., Robust estimation of mean squared error of small area estimators, J. Amer. Statist. Assoc., 90, 758-766 (1995) · Zbl 0826.62008 [6] Lindley, D. V., Discussion of Professor Stein’s paper, J. Roy. Statist. Soc. B, 24, 265-296 (1962) [7] Louis, T. A., Estimating a population of parameter values using Bayes and empirical Bayes methods, J. Amer. Statist. Assoc., 79, 393-398 (1984) [8] Morris, C., Parametric empirical Bayes confidence intervals, (Box, G. E.P.; Leonard, T.; Jeff Wu, C. F., Scientific Inference, Data Analysis, and Robustness (1981), Academic Press: Academic Press New York), 25-50 [9] Prasad, N. G.N.; Rao, J. N.K., The estimation of the mean squared error of small-area estimators, J. Amer. Statist. Assoc., 85, 163-171 (1990) · Zbl 0719.62064 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.