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Bayesian nonparametric point estimation under a conjugate prior


  • Li, Xuefeng
  • Zhao, Linda H.


Estimation of a nonparametric regression function at a point is considered. The function is assumed to lie in a Sobolev space, Sq, of order q. The asymptotic squared-error performance of Bayes estimators corresponding to Gaussian priors is investigated as the sample size, n, increases. It is shown that for any such fixed prior on Sq the Bayes procedures do not attain the optimal minimax rate over balls in Sq. This result complements that in Zhao (Ann. Statist. 28 (2000) 532) for estimating the entire regression function, but the proof is rather different.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:58:y:2002:i:1:p:23-30

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    Cited by:

    1. 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.


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