WIAS Preprint No. 191, (1995)

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


  • Lepskii, Oleg
  • Mammen, Enno
  • Spokoiny, Vladimir G.

2010 Mathematics Subject Classification

  • 62G07 62G20


  • Besov spaces, spatial adaptation, minimax rate of convergence, white noise model, kernel estimation


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.

Appeared in

  • Annals of Statistics, 25 (1997) No. 3, pp. 929-947

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