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

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  • Shi-Shun Zhao
  • Jian Tao
  • Ning-Zhong Shi
  • Nan Lin

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.

Suggested Citation

  • Shi-Shun Zhao & Jian Tao & Ning-Zhong Shi & Nan Lin, 2015. "A Note on the Comparison of the Stein Estimator and the James-Stein Estimator," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(16), pages 3363-3374, August.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:16:p:3363-3374
    DOI: 10.1080/03610926.2013.799693
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