Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 44, 2015 - Issue 16
Submit an article Journal homepage
265
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

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

Shi-Shun ZhaoCollege of Mathematics, Jilin University, Changchun, China
,
Jian TaoKey Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, ChinaCorrespondence[email protected]
,
Ning-Zhong ShiKey Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
&
Nan LinDepartment of Mathematics, Washington University in Saint Louis, Saint Louis, Missouri, USA
Pages 3363-3374 | Received 08 Aug 2012, Accepted 08 Apr 2013, Published online: 01 Sep 2015

References

  • Anderson, T.W. (1984). An Introduction to Multivariate Statistical Analysis. 2nd ed. New York: John Wiley & Sons.
  • Arashi, M., Tabatabaey, S. M.M. (2010). A note on classical Stein-type estimators in elliptically contoured models. J. Statist. Plann. Infer. 140:1206–1213.
  • Baranchik, A.J. (1970). A family of minimax estimators of the mean of a multivariate normal distribution. Ann. Mathemat. Statist. 41:642–645.
  • Brandwein, A.C., Strawderman, W.E. (1990). Stein estimation: The spherically symmetric case. Statist. Sci. 5:356–369.
  • Brandwein, A.C., Strawderman, W.E. (1991). Generalizations of James-Stein estimators under spherical symmetry. Ann. Statist. 19:1639–1650.
  • Brown, L.D., Fu, X., Zhao, L.H. (2011). Confidence intervals for nonparametric regression. J. Nonparametric Statist. 23:149–163.
  • Casella, G. (1985). An introduction to empirical Bayes data analysis. Amer. Statistician 39:83–87.
  • Efron, B., Morris, C. (1973). Stein’s estimation rule and its competitors—an empirical Bayes approach. J. Amer. Statist. Assoc. 68:117–130.
  • Gao, J.X., Hitchcock, D.B. (2010). James-Stein shrinkage to improve k-means cluster analysis. Computat. Statist. Data Anal. 54:2113–2127.
  • Green, E.J., Strawderman, W.E. (1991). A James-Stein type estimator for combining unbiased and possibly biased estimators. J. Amer. Statist. Assoc. 86:1001–1006.
  • James, W., Stein, C. (1961). Estimation with quadratic loss. Proc. Fourth Berkeley Symp. Mathemat. Statist. Probab., University of California Press, 1:361–379.
  • Judge, G.G., Mittelhammer, R.C. (2004). A semiparametric basis for combining estimation problems under quadratic loss. J. Amer. Statist. Assoc. 99:479–487.
  • Kumar, S., Tripathi, Y.M., Misra, N. (2005). James-Stein type estimators for ordered normal means. J. Statist. Computat. Simul. 75:501–511.
  • Maruyama, Y., Strawderman, W.E. (2005). Necessary conditions for dominating the James-Stein estimator. Ann. Instit. Statist. Math. 57:157–165.
  • Privault, N., Réveillac, A. (2008). Stein estimation for the drift of Gaussian processes using the Malliavin calculus. Ann. Statist. 36:2531–2550.
  • Ralescu, S., Brandwein, A.C., Strawderman, W.E. (1992). Stein estimation for nonnormal spherically symmetric location families in three dimensions. J. Multivariate Anal. 42:35–50.
  • Senda, M., Taniguchi, M. (2006). James-Stein estimators for time series regression models. J. Multivariate Anal. 97:1984–1996.
  • Shalabh, Toutenburg, H., Heumann, C. (2009). Stein-rule estimation under an extended balanced loss function. J. Statist. Computat. Simul. 79:1259–1273.
  • Shao, P.Y.-S., Strawderman, W.E. (1994). Improving on the James-Stein positive-part estimator. Ann. Statist. 22:1517–1538.
  • Srivastava, M.S., Bilodeau, M. (1989). Stein estimation under elliptical distributions. J. Multivariate Anal. 28:247–259.
  • Stein, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. Third Berkeley Symp. Mathemat. Statist. Probab., University of California Press, 1:197–206.
  • Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9:1135–1151.
  • Taniguchi, M., Hirukawa, J. (2005). The Stein-James estimator for short- and long-memory Gaussian processes. Biometrika 92:737–746.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.