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- Title
A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function.
- Authors
Efromovich, Sam
- 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.
- Subjects
MATHEMATICS; STATISTICS; CHEBYSHEV approximation; REGRESSION analysis; ESTIMATION theory; MATHEMATICAL statistics
- Publication
Scandinavian Journal of Statistics, 2005, Vol 32, Issue 1, p133
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2005.00419.x