The Annals of Statistics

Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors

O. V. Lepski, E. Mammen, and V. G. Spokoiny

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 25, Number 3 (1997), 929-947.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362731

Digital Object Identifier
doi:10.1214/aos/1069362731

Mathematical Reviews number (MathSciNet)
MR1447734

Zentralblatt MATH identifier
0885.62044

Subjects
Primary: 62G07: Density estimation

Keywords
Kernel estimate bandwidth choice Besov spaces spatial adaptation minimax rate of convergence

Citation

Lepski, O. V.; Mammen, E.; Spokoiny, V. G. Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 (1997), no. 3, 929--947. doi:10.1214/aos/1069362731. https://projecteuclid.org/euclid.aos/1069362731


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