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June 1997 Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors
O. V. Lepski, E. Mammen, V. G. Spokoiny
Ann. Statist. 25(3): 929-947 (June 1997). DOI: 10.1214/aos/1069362731

Abstract

A new variable bandwidth selector for kernel estimation is proposed. The application of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over Besov classes. This implies that the procedure adapts to spatially inhomogeneous smoothness. In particular, the estimates share optimality properties with wavelet estimates based on thresholding of empirical wavelet coefficients.

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O. V. Lepski. E. Mammen. V. G. Spokoiny. "Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors." Ann. Statist. 25 (3) 929 - 947, June 1997. https://doi.org/10.1214/aos/1069362731

Information

Published: June 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0885.62044
MathSciNet: MR1447734
Digital Object Identifier: 10.1214/aos/1069362731

Subjects:
Primary: 62G07

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 3 • June 1997
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