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Estimation of a Normal Mean Vector II

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Shrinkage Estimation

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Abstract

As we saw in Chap. 2, the frequentist paradigm is well suited for risk evaluations, but is less useful for estimator construction. It turns out that the Bayesian approach is complementary, as it is well suited for the construction of possibly optimal estimators. In this chapter we take a Bayesian view of minimax shrinkage estimation. In Sect. 3.1 we derive a general sufficient condition for minimaxity of Bayes and generalized Bayes estimators in the known variance case, we also illustrate the theory with numerous examples.

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Author information

Authors and Affiliations

  1. Mathématiques, BP 12, Université de Rouen, St-Étienne-du-Rouvray, France

    Dominique Fourdrinier

  2. Department of Statistics, Rutgers University, Piscataway, NJ, USA

    William E. Strawderman

  3. Department of Statistical Science, Cornell University, Ithaca, NY, USA

    Martin T. Wells

Authors
  1. Dominique Fourdrinier
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  2. William E. Strawderman
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  3. Martin T. Wells
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Fourdrinier, D., Strawderman, W.E., Wells, M.T. (2018). Estimation of a Normal Mean Vector II. In: Shrinkage Estimation. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-02185-6_3

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