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Shrinkage estimation for convex polyhedral cones

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  • Amirdjanova, Anna
  • Woodroofe, Michael
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    Abstract

    Estimation of a multivariate normal mean is considered when the latter is known to belong to a convex polyhedron. It is shown that shrinking the maximum likelihood estimator towards an appropriate target can reduce mean squared error. The proof combines an unbiased estimator of a risk difference with some geometrical considerations. When applied to the monotone regression problem, the main result shows that shrinking the maximum likelihood estimator towards modifications that have been suggested to alleviate the spiking problem can reduce mean squared error.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4D97J25-1/2/fd1352b769016c8c4f6472b63bfbce05
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 70 (2004)
    Issue (Month): 1 (October)
    Pages: 87-94

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    Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:87-94

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    Related research

    Keywords: Degrees of freedom Maximum likelihood estimator Mean squared error Primal-dual bases Projections Stein's Identity Target estimator;

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    1. 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.
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