Wavelet regression in random design with heteroscedastic dependent errors
| Autor: | Marc Raimondo, Rafał Kulik |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Statistics::Theory long range dependence Heteroscedasticity thresholding Mathematics - Statistics Theory Statistics Theory (math.ST) 02 engineering and technology random design wavelets 01 natural sciences 62G05 (Primary) 62G08 62G20 (Secondary) 010104 statistics & probability Adaptive estimation Wavelet 62G08 FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Range (statistics) Applied mathematics 62G05 0101 mathematics 62G20 Mathematics warped wavelets 020206 networking & telecommunications Regression analysis Function (mathematics) Nonparametric regression Distribution function Rate of convergence nonparametric regression shape estimation Statistics Probability and Uncertainty maxiset |
| Zdroj: | Ann. Statist. 37, no. 6A (2009), 3396-3430 |
| ISSN: | 0090-5364 |
| DOI: | 10.1214/09-aos684 |
| Popis: | We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, $f\in\mathcal{B}^s_{\pi,r}$, and for a variety of $L^p$ error measures. We consider error distributions with Long-Range-Dependence parameter $\alpha,02$, it is seen that there are three rate phases, namely the dense, sparse and long range dependence phase, depending on the relative values of $s,p,\pi$ and $\alpha$. Furthermore, we show that long range dependence does not come into play for shape estimation $f-\int f$. The theory is illustrated with some numerical examples. Comment: Published in at http://dx.doi.org/10.1214/09-AOS684 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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