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.
Publié le : 1992-06-14
Classification:
Radon transform,
Riesz transform,
deconvolution,
partial deconvolution,
minimax kernels,
boundary kernels,
minimax linear estimation,
minimax risk,
white noise model,
Gaussian experiments,
62G07,
62C20
@article{1176348665,
author = {Donoho, David L. and Low, Mark G.},
title = {Renormalization Exponents and Optimal Pointwise Rates of Convergence},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 944-970},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348665}
}
Donoho, David L.; Low, Mark G. Renormalization Exponents and Optimal Pointwise Rates of Convergence. Ann. Statist., Tome 20 (1992) no. 1, pp. 944-970. http://gdmltest.u-ga.fr/item/1176348665/