A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function
A blockwise shrinkage is a popular adaptive procedure for non-parametric series estimates. It possesses an impressive range of asymptotic properties, and there is a vast pool of blocks and shrinkage procedures used. Traditionally these estimates are studied via upper bounds on their risks. This article suggests the study of these adaptive estimates via non-asymptotic lower bounds established for a spike underlying function that plays a pivotal role in the wavelet and minimax statistics. While upper-bound inequalities help the statistician to find sufficient conditions for a desirable estimation, the non-asymptotic lower bounds yield necessary conditions and shed a new light on the popular method of adaptation. The suggested method complements and knits together two traditional techniques used in the analysis of adaptive estimates: a numerical study and an asymptotic minimax inference. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..
Year of publication: |
2005
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Authors: | EFROMOVICH, SAM |
Published in: |
Scandinavian Journal of Statistics. - Danish Society for Theoretical Statistics, ISSN 0303-6898. - Vol. 32.2005, 1, p. 133-158
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Publisher: |
Danish Society for Theoretical Statistics Finnish Statistical Society Norwegian Statistical Association Swedish Statistical Association |
Saved in:
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