Locally adaptive wavelet empirical Bayes estimation of a location parameter

    Authors

    M. Pensky

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Ann. Inst. Stat. Math.

    Keywords

    empirical Bayes estimation; adaptive estimation; wavelet; posterior and; prior risks; DENSITY-ESTIMATION; CURVE ESTIMATION; ERROR; RATES; Statistics & Probability

    Abstract

    The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier.

    Journal Title

    Annals of the Institute of Statistical Mathematics

    Volume

    54

    Issue/Number

    1

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    83

    Last Page

    99

    WOS Identifier

    WOS:000174797700006

    ISSN

    0020-3157

    Share

    COinS