Wavelet Estimation For Samples With Random Uniform Design
Tony Cai and Lawrence Brown
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Abstract:
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.
- Paper:
pdf file.
- Other related paper:
Cai, T. & Brown, L.D. (1998).
Wavelet shrinkage for nonequispaced samples.
The Annals of Statistics 26, 1783-1799.