Electronic Journal of Statistics

Wavelet block thresholding for samples with random design: a minimax approach under the Lp risk

Christophe Chesneau

Full-text: Open access

Abstract

We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the Lp risk with p2 over Besov balls. We prove that it is near optimal and that it achieves better rates of convergence than the conventional term-by-term estimators (hard, soft,…).

Article information

Source
Electron. J. Statist., Volume 1 (2007), 331-346.

Dates
First available in Project Euclid: 30 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1188481984

Digital Object Identifier
doi:10.1214/07-EJS067

Mathematical Reviews number (MathSciNet)
MR2336037

Zentralblatt MATH identifier
1140.62315

Subjects
Primary: 62G07: Density estimation 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 62G20: Asymptotic properties

Keywords
Regression with random design wavelets block thresholding

Citation

Chesneau, Christophe. Wavelet block thresholding for samples with random design: a minimax approach under the L p risk. Electron. J. Statist. 1 (2007), 331--346. doi:10.1214/07-EJS067. https://projecteuclid.org/euclid.ejs/1188481984


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