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Zbl 0940.62037
Cai, T.Tony; Brown, Lawrence D.
Wavelet estimation for samples with random uniform design. (English)
[J] Stat. Probab. Lett. 42, No.3, 313-321 (1999). ISSN 0167-7152

Summary: We show that for nonparametric regression if the samples have random uniform design, the wavelet method with universal thresholding can be applied directly to the samples as if they were equispaced. The resulting estimator achieves within a logarithmic factor from the minimax rate of convergence over a family of Hölder classes. Simulation result is also discussed.

MSC 2000:: *62G08 Nonparametric regression
62G20 Nonparametric asymptotic efficiency
42C40 Wavelets

Keywords: minimax; adaptivity; Hölder classes

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Zentralblatt MATH Berlin [Germany]