Statistical Science

Comment: Empirical Bayes Interval Estimation

Wenhua Jiang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


This is a contribution to the discussion of the enlightening paper by Professor Efron. We focus on empirical Bayes interval estimation. We discuss the oracle interval estimation rules, the empirical Bayes estimation of the oracle rule and the computation. Some numerical results are reported.

Article information

Statist. Sci., Volume 34, Number 2 (2019), 219-223.

First available in Project Euclid: 19 July 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Empirical Bayes interval estimation oracle rule generalized MLE


Jiang, Wenhua. Comment: Empirical Bayes Interval Estimation. Statist. Sci. 34 (2019), no. 2, 219--223. doi:10.1214/19-STS708.

Export citation


  • Efron, B. (2014). Two modeling strategies for empirical Bayes estimation. Statist. Sci. 29 285–301.
  • Efron, B. (2016). Empirical Bayes deconvolution estimates. Biometrika 103 1–20.
  • Hannan, J. F. and Robbins, H. (1955). Asymptotic solutions of the compound decision problem for two completely specified distributions. Ann. Math. Stat. 26 37–51.
  • Jiang, W. and Zhang, C.-H. (2009). General maximum likelihood empirical Bayes estimation of normal means. Ann. Statist. 37 1647–1684.
  • Jiang, W. and Zhang, C.-H. (2016). Generalized likelihood ratio test for normal mixtures. Statist. Sinica 26 955–978.
  • Kiefer, J. and Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Stat. 27 887–906.
  • Koenker, R. and Mizera, I. (2014). Convex optimization, shape constraints, compound decisions, and empirical Bayes rules. J. Amer. Statist. Assoc. 109 674–685.
  • Laird, N. M. and Louis, T. A. (1987). Empirical Bayes confidence intervals based on bootstrap samples. J. Amer. Statist. Assoc. 82 739–757.
  • Morris, C. N. (1983). Parametric empirical Bayes inference: Theory and applications. J. Amer. Statist. Assoc. 78 47–65.
  • Robbins, H. (1951). Asymptotically subminimax solutions of compound decision problems. In Proc. Second Berkeley Symp. Math. Statist. Probab. 1 131–148. Univ. California Press, Berkeley, CA.
  • Robbins, H. (1956). An empirical Bayes approach to statistics. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 19541955 1 157–163. Univ. California Press, Berkeley and Los Angeles.
  • Vardi, Y., Shepp, L. A. and Kaufman, L. (1985). A statistical model for positron emission tomography. J. Amer. Statist. Assoc. 80 8–20.

See also