Data-driven wavelet-Fisz methodology for nonparametric function estimation
| dc.creator | Fryzlewicz, Piotr | |
| dc.date | 2007-11-06 | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:06:30Z | |
| dc.date.available | 2026-07-07T10:06:30Z | |
| dc.description | We propose a wavelet-based technique for the nonparametric estimation of functions contaminated with noise whose mean and variance are linked via a possibly unknown variance function. Our method, termed the data-driven wavelet-Fisz technique, consists of estimating the variance function via a Nadaraya-Watson estimator, and then performing a wavelet thresholding procedure which uses the estimated variance function and local means of the data to set the thresholds at a suitable level. We demonstrate the mean-square near-optimality of our wavelet estimator over the usual range of Besov classes. To achieve this, we establish an exponential inequality for the Nadaraya-Watson variance function estimator. We discuss various implementation issues concerning our wavelet estimator, and demonstrate its good practical performance. We also show how it leads to a new wavelet-domain data-driven variance-stabilising transform. Our estimator can be applied to a variety of problems, including the estimation of volatilities, spectral densities and Poisson intensities, as well as to a range of problems in which the distribution of the noise is unknown. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-EJS139 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0711.0883 | |
| dc.identifier | http://arxiv.org/abs/0711.0883 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 863-896 | |
| dc.identifier | doi:10.1214/07-EJS139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170346 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G08 (Primary) 62G05, 62G20 (Secondary) | |
| dc.title | Data-driven wavelet-Fisz methodology for nonparametric function estimation | |
| dc.type | text |