Renormalization Exponents and Optimal Pointwise Rates of Convergence
The Annals of Statistics · 1992 · Volume 20 · Issue 2
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.
Keywords
62C20; 62G07; boundary kernels; Deconvolution; Gaussian experiments; minimax kernels; minimax linear estimation; minimax risk; partial deconvolution; Radon transform; Riesz transform; White noise model;
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