Lepski, O. V.; Mammen, E.; Spokoiny, V. G. Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors. (English) Zbl 0885.62044 Ann. Stat. 25, No. 3, 929-947 (1997). Summary: 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. Cited in 4 ReviewsCited in 101 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference Keywords:Besov spaces; spatial adaptation; minimax rate of convergence; white noise model; kernel estimation PDFBibTeX XMLCite \textit{O. V. Lepski} et al., Ann. Stat. 25, No. 3, 929--947 (1997; Zbl 0885.62044) Full Text: DOI