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Confidence Intervals for Adaptive Regression Estimation on the Besov Spaces

Anatoli Juditsky 1 Sophie Lambert-Lacroix 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : The problem of adaptive estimation of the regression function f from noisy observations is concerned. A confidence interval for the L_2-error for wavelet adaptive estimator is provided. We show that if f belongs to a Besov class, the proposed confidence interval is minimax.
Keywords : WAVELET ESTIMATORS CONFIDENCE INTERVALS ADAPTIVE ESTIMATION NONPARAMETRIC REGRESSION
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https://hal.inria.fr/inria-00073030
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Submitted on : Wednesday, May 24, 2006 - 11:39:59 AM
Last modification on : Friday, February 4, 2022 - 3:31:21 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:15:32 PM

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Anatoli Juditsky, Sophie Lambert-Lacroix. Confidence Intervals for Adaptive Regression Estimation on the Besov Spaces. [Research Report] RR-3643, INRIA. 1999. ⟨inria-00073030⟩

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