The Annals of Statistics

Renormalization Exponents and Optimal Pointwise Rates of Convergence

David L. Donoho and Mark G. Low

Full-text: Open access

Abstract

Simple renormalization arguments can often be used to calculate optimal rates of convergence for estimating linear functionals from indirect measurements contaminated with white noise. This allows one to quickly identify optimal rates for certain problems of density estimation, nonparametric regression, signal recovery and tomography. Optimal kernels may also be derived from renormalization; we give examples for deconvolution and tomography.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 944-970.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348665

Digital Object Identifier
doi:10.1214/aos/1176348665

Mathematical Reviews number (MathSciNet)
MR1165601

Zentralblatt MATH identifier
0797.62032

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62C20: Minimax procedures

Keywords
Radon transform Riesz transform deconvolution partial deconvolution minimax kernels boundary kernels minimax linear estimation minimax risk white noise model Gaussian experiments

Citation

Donoho, David L.; Low, Mark G. Renormalization Exponents and Optimal Pointwise Rates of Convergence. Ann. Statist. 20 (1992), no. 2, 944--970. doi:10.1214/aos/1176348665. https://projecteuclid.org/euclid.aos/1176348665


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