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Renormalization Exponents and Optimal Pointwise Rates of Convergence

David L. Donoho and Mark G. Low
The Annals of Statistics
Vol. 20, No. 2 (Jun., 1992), pp. 944-970
Stable URL: http://www.jstor.org/stable/2241992
Page Count: 27
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Renormalization Exponents and Optimal Pointwise Rates of Convergence
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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.

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