Optimal Adaptive Estimation of a Quadratic Functional
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Statistics Papers
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adaptation
block thresholding
quadratic functionals
wavelets
white noise model
Statistics and Probability
block thresholding
quadratic functionals
wavelets
white noise model
Statistics and Probability
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Cai, T. Tony
Low, Mark G
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Abstract
Adaptive estimation of a quadratic functional over both Besov and Lp balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and Lp balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and Lp balls in the sense that it attains certain constrained risk bounds.
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2006-01-01
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The Annals of Statistics