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Stokes’ theorem, Stein’s identity and completeness

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  • Fourdrinier, Dominique
  • Strawderman, William E.

Abstract

We study the relation between Stein’s theorem and Stokes’ theorem (or the divergence theorem) and show, using completeness of certain exponential families, that they are equivalent, in a certain sense, by using each to prove a version of the other.

Suggested Citation

  • Fourdrinier, Dominique & Strawderman, William E., 2016. "Stokes’ theorem, Stein’s identity and completeness," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 224-231.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:224-231
    DOI: 10.1016/j.spl.2015.11.003
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    References listed on IDEAS

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    1. Berger, James O., 1978. "Minimax estimation of a multivariate normal mean under polynomial loss," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 173-180, June.
    2. Fourdrinier, Dominique & Strawderman, William E., 2008. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 735-750, April.
    3. Ann Brandwein & Stefan Ralescu & William Strawderman, 1993. "Shrinkage estimators of the location parameter for certain spherically symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 551-565, September.
    4. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    5. Fourdrinier, Dominique & Strawderman, William E. & Wells, Martin T., 2003. "Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 24-39, April.
    Full references (including those not matched with items on IDEAS)

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