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February 2000 Adaptive confidence interval for pointwise curve estimation
Dominique Picard, Karine Tribouley
Ann. Statist. 28(1): 298-335 (February 2000). DOI: 10.1214/aos/1016120374

Abstract

We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around $f (x_0)$, in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function $f$; it is also efficient for functions with a low degree of regularity.

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Dominique Picard. Karine Tribouley. "Adaptive confidence interval for pointwise curve estimation." Ann. Statist. 28 (1) 298 - 335, February 2000. https://doi.org/10.1214/aos/1016120374

Information

Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62331
MathSciNet: MR1762913
Digital Object Identifier: 10.1214/aos/1016120374

Subjects:
Primary: 26G30 , 62C20 , 62G07 , 62G15

Keywords: adaptive estimation , Confidence interval , Edgeworth expansion , Wavelet methods

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2000
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