Locally adaptive estimation of evolutionary wavelet spectra
| dc.creator | Van Bellegem, Sébastien | |
| dc.creator | von Sachs, Rainer | |
| dc.date | 2008-08-11 | |
| dc.date.accessioned | 2026-07-07T09:55:57Z | |
| dc.date.available | 2026-07-07T09:55:57Z | |
| dc.description | We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on scales. We propose a pointwise adaptive estimator of the time-varying spectrum. The behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AOS524 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0808.1452 | |
| dc.identifier | http://arxiv.org/abs/0808.1452 | |
| dc.identifier | Annals of Statistics 2008, Vol. 36, No. 4, 1879-1924 | |
| dc.identifier | doi:10.1214/07-AOS524 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166811 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62M10 (Primary) 60G15, 62G10, 62G05 (Secondary) | |
| dc.title | Locally adaptive estimation of evolutionary wavelet spectra | |
| dc.type | text |