The Annals of Statistics

Adaptive confidence interval for pointwise curve estimation

Dominique Picard and Karine Tribouley

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 28, Number 1 (2000), 298-335.

Dates
First available in Project Euclid: 14 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1016120374

Digital Object Identifier
doi:10.1214/aos/1016120374

Mathematical Reviews number (MathSciNet)
MR1762913

Zentralblatt MATH identifier
1106.62331

Subjects
Primary: 62C20: Minimax procedures 62G07: Density estimation 62G15: Tolerance and confidence regions 26G30

Keywords
Adaptive estimation Confidence interval Edgeworth expansion Wavelet methods

Citation

Picard, Dominique; Tribouley, Karine. Adaptive confidence interval for pointwise curve estimation. Ann. Statist. 28 (2000), no. 1, 298--335. doi:10.1214/aos/1016120374. https://projecteuclid.org/euclid.aos/1016120374


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