On the lower bounds for mean square error of empirical bayes estimators

Penskaya, M. Ya.

doi:10.1007/bf02368737

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2013

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“…Only some particular cases of the problem were investigated. Specifically, Penskaya (1995) obtain lower bounds for the posterior risk of nonparametric empirical Bayes estimators of a location parameter. Li, Gupta and Liese (2005) obtained lower bounds for the risk of empirical Bayes estimators in the exponential families.…”

Section: 4)mentioning

confidence: 99%

Adaptive nonparametric empirical Bayes estimation via wavelet series: The minimax study

Benhaddou

Pensky

2013

Journal of Statistical Planning and Inference

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In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which takes advantage of the flexibility of the wavelet techniques. We present an empirical Bayes estimator as a wavelet series expansion and estimate coefficients by minimizing the prior risk of the estimator. As a result, estimation of wavelet coefficients requires solution of a well-posed low-dimensional sparse system of linear equations. The dimension of the system depends on the size of wavelet support and smoothness of the Bayes estimator. An adaptive choice of the resolution level is carried out using Lepski (1997) method. The method is computationally efficient and provides asymptotically optimal adaptive EB estimators. The theory is supplemented by numerous examples.

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Section: 4)mentioning

confidence: 99%