Open Access
August 2007 A ridge-parameter approach to deconvolution
Peter Hall, Alexander Meister
Ann. Statist. 35(4): 1535-1558 (August 2007). DOI: 10.1214/009053607000000028


Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely supported and its characteristic function does not ever vanish. Even in these settings, optimal convergence rates are achieved by kernel estimators only when the kernel is chosen to adapt to the unknown smoothness of the target distribution. In this paper we suggest alternative ridge methods, not involving kernels in any way. We show that ridge methods (a) do not require the assumption that the error-distribution characteristic function is nonvanishing; (b) adapt themselves remarkably well to the smoothness of the target density, with the result that the degree of smoothness does not need to be directly estimated; and (c) give optimal convergence rates in a broad range of settings.


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Peter Hall. Alexander Meister. "A ridge-parameter approach to deconvolution." Ann. Statist. 35 (4) 1535 - 1558, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1147.62031
MathSciNet: MR2351096
Digital Object Identifier: 10.1214/009053607000000028

Primary: 62F05 , 62G07

Keywords: cross-validation , density deconvolution , errors in variables , kernel methods , Minimax optimality , optimal convergence rates , smoothing-parameter choice

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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