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A nonparametric empirical Bayes approach to adaptive minimax estimation

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  • Jiang, Wenhua
  • Zhang, Cun-Hui

Abstract

The general maximum likelihood empirical Bayes (GMLEB) method has been proven to possess optimal properties and demonstrated to have superior numerical performance in the Gaussian sequence model. Although it is known that nonparametric function estimation and the Gaussian sequence models are closely related, implementation of the GMLEB in function estimation problems still awaits careful analysis. In this paper, we consider adaptive estimation to inhomogeneous smoothness. We study the extent to which the optimality properties of the GMLEB can be carried out from the Gaussian sequence model to nonparametric function estimation. We demonstrate the proposed method’s superior performance in large sample size settings.

Suggested Citation

  • Jiang, Wenhua & Zhang, Cun-Hui, 2013. "A nonparametric empirical Bayes approach to adaptive minimax estimation," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 82-95.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:82-95
    DOI: 10.1016/j.jmva.2013.07.013
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    References listed on IDEAS

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    1. Jiang, Wenhua, 2013. "On regularized general empirical Bayes estimation of normal means," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 54-62.
    2. T. Tony Cai & Mark Low & Linda Zhao, 2009. "Sharp adaptive estimation by a blockwise method," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 839-850.
    3. Felix Abramovich & Vadim Grinshtein & Athanasia Petsa & Theofanis Sapatinas, 2010. "On Bayesian testimation and its application to wavelet thresholding," Biometrika, Biometrika Trust, vol. 97(1), pages 181-198.
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