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A note on improving on a vector of coordinate-wise estimators of non-negative means via shrinkage

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  • Chang, Yuan-Tsung
  • Matsuda, Takeru
  • Strawderman, William E.

Abstract

We study improved shrinkage estimation of a vector of non-negative means. We concentrate on the Gaussian case with known scale, but do not necessarily assume the initial estimator is minimax. As a result, we find improved shrinkage estimators in fewer than 3 dimension in certain cases. Generalized Bayes estimators which may be improved via shrinkage in 1 and 2 dimensions illustrate the result. We also consider improved positive part estimators.

Suggested Citation

  • Chang, Yuan-Tsung & Matsuda, Takeru & Strawderman, William E., 2019. "A note on improving on a vector of coordinate-wise estimators of non-negative means via shrinkage," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 143-150.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:143-150
    DOI: 10.1016/j.spl.2019.06.005
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2008. "Stein's phenomenon in estimation of means restricted to a polyhedral convex cone," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 141-164, January.
    2. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    3. Yogesh Tripathi & Somesh Kumar, 2007. "Estimating a positive normal mean," Statistical Papers, Springer, vol. 48(4), pages 609-629, October.
    4. Chang, Yuan-Tsung & Strawderman, William E., 2017. "Simultaneous estimation of p positive normal means with common unknown variance," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 83-89.
    5. Ouassou, Idir & Strawderman, William E., 2002. "Estimation of a parameter vector restricted to a cone," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 121-129, January.
    6. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    7. Fourdrinier, Dominique & Ouassou, Idir & Strawderman, William E., 2003. "Estimation of a parameter vector when some components are restricted," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 14-27, July.
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