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On the posterior pointwise convergence rate of a Gaussian signal under a conjugate prior

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  • Babenko, Alexandra
  • Belitser, Eduard

Abstract

We consider the problem of Bayes estimation of a linear functional of the signal in the Gaussian white noise mode, under the assumption that the unknown signal is from a Sobolev smoothness class. We propose a family of conjugate (Gaussian) priors and prove that the resulting Bayes estimators are rate minimax from both frequentist and Bayes perspectives. Finally, we show that the posterior distribution of the functional concentrates around the true value of the functional with the minimax rate uniformly over the Sobolev class.

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  • Babenko, Alexandra & Belitser, Eduard, 2009. "On the posterior pointwise convergence rate of a Gaussian signal under a conjugate prior," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 670-675, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:670-675
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    References listed on IDEAS

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    1. Li, Xuefeng & Zhao, Linda H., 2002. "Bayesian nonparametric point estimation under a conjugate prior," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 23-30, May.
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    Cited by:

    1. Babenko, Alexandra & Belitser, Eduard, 2011. "Lower bound for the oracle projection posterior convergence rate," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 175-180, February.
    2. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve prior," Working Papers 2013-19, Center for Research in Economics and Statistics.
    3. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve Prior," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 549-570, September.

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