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

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

Research output: Contribution to journalArticlepeer-review

176 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)929-947
Number of pages19
JournalAnnals of Statistics
Volume25
Issue number3
DOIs
Publication statusPublished - Jun 1997
Externally publishedYes

Keywords

  • Bandwidth choice
  • Besov spaces
  • Kernel estimate
  • Minimax rate of convergence
  • Spatial adaptation

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