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A Study of Blockwise Wavelet Estimates Via Lower Bounds for a Spike Function
Author(s) -
EFROMOVICH SAM
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00419.x
Subject(s) - minimax , mathematics , upper and lower bounds , range (aeronautics) , wavelet , function (biology) , parametric statistics , spike (software development) , inference , mathematical optimization , statistics , computer science , mathematical analysis , artificial intelligence , materials science , evolutionary biology , composite material , biology , software engineering
. 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.