Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means
Brown, Lawrence D. ; Greenshtein, Eitan
Ann. Statist., Tome 37 (2009) no. 1, p. 1685-1704 / Harvested from Project Euclid
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We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations Yi∼N(μi, 1), i=1, …, n. ¶ Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂−μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. ¶ Our asymptotics is of a triangular array; that is, we allow the distribution G to depend on n. Thus, our theoretical asymptotic results are also meaningful in situations where the vector μ is sparse and the proportion of zero coordinates approaches 1. ¶ We demonstrate the performance of our estimator in simulations, emphasizing sparse setups. In “moderately-sparse” situations, our procedure performs very well compared to known procedures tailored for sparse setups. It also adapts well to nonsparse situations.
Publié le : 2009-08-15
Classification:  Empirical Bayes,  compound decision,  62C12,  62C25 
@article{1245332829,
     author = {Brown, Lawrence D. and Greenshtein, Eitan},
     title = {Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means},
     journal = {Ann. Statist.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1685-1704},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245332829}
}

Brown, Lawrence D.; Greenshtein, Eitan. Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means. Ann. Statist., Tome 37 (2009) no. 1, pp.  1685-1704. http://gdmltest.u-ga.fr/item/1245332829/