Rates of convergence of empirical Bayes tests for a normal mean

    Authors

    M. Pensky

    Comments

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    Abbreviated Journal Title

    J. Stat. Plan. Infer.

    Keywords

    PARAMETER EXPONENTIAL FAMILY; GEOMETRIZING RATES; Statistics & Probability

    Abstract

    In the present paper, the EB two-action problem under the linear error loss is considered for the family of normal distributions with the location parameter. The purpose is to establish the upper and lower bounds for the risk. A monotone adaptive empirical Bayes test is constructed with the regret risk converging to zero at a rate of O(n(-1)(ln n)(3/2)). The lower bound for the risk of the form O(n(-1)(ln n)(1/2)(ln ln n)(-1)) is derived. In the author's opinion, the (ln n ln ln n) times difference between the lower and the upper bounds is due not to the fact that the estimator suggested in the paper is not optimal but to the fact that the lower bound is not exact. (C) 2002 Elsevier Science B.V. All rights reserved.

    Journal Title

    Journal of Statistical Planning and Inference

    Volume

    111

    Issue/Number

    1-2

    Publication Date

    1-1-2003

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    181

    Last Page

    196

    WOS Identifier

    WOS:000180324200013

    ISSN

    0378-3758

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