A Note on the Comparison of the Stein Estimator and the James-Stein Estimator

Shi-Shun Zhao, Jian Tao, Ning-Zhong Shi and Nan Lin

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 16, 3363-3374

Abstract: The seminal work of Stein (1956) showed that the maximum likelihood estimator (MLE) of the mean vector of a p-dimensional multivariate normal distribution is inadmissible under the squared error loss function when p ⩾ 3 and proposed the Stein estimator that dominates the MLE. Later, James and Stein (1961) proposed the James-Stein estimator for the same problem and received much more attention than the original Stein estimator. We re-examined the Stein estimator and conducted an analytic comparison with the James-Stein estimator. We found that the Stein estimator outperforms the James-Stein estimator under certain scenarios and derived the sufficient conditions.

Date: 2015
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DOI: 10.1080/03610926.2013.799693

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