The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space B s p, q is proved under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a
Wavelet regression for random or irregular design
β Scribed by Anestis Antoniadis; Dinh Tuan Pham
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 865 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0167-9473
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, wavelet regression estimators are introduced, both in the random and the irregular design cases and without the restriction that the sample size is a power of two. A fast computational algorithm for approximating the empirical counterpart of the scaling and wavelet coefficients, is developed. The convergence rate of the estimator is established. The method is illustrated by some simulations and by a real example.
π SIMILAR VOLUMES
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 ove