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A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function

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  • SAM EFROMOVICH

Abstract

. 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.

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  • Sam Efromovich, 2005. "A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 133-158, March.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:1:p:133-158
    DOI: 10.1111/j.1467-9469.2005.00419.x
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