Adaptive nonparametric empirical Bayes estimation via wavelet series: The minimax study
Abbreviated Journal Title
J. Stat. Plan. Infer.
Adaptivity; Empirical Bayes estimation; Wavelets; Convergence rate; EXPONENTIAL-FAMILIES; CONVERGENCE-RATES; PARAMETER; POPULATION; LOCATION; TESTS; Statistics & Probability
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 et al. (1997) method. The method is computationally efficient and provides asymptotically optimal adaptive EB estimators. The theory is supplemented by numerous examples. (C) 2013 Elsevier B.V. All rights reserved.
Journal of Statistical Planning and Inference
"Adaptive nonparametric empirical Bayes estimation via wavelet series: The minimax study" (2013). Faculty Bibliography 2010s. 3695.