Warped Wavelet and Vertical Thresholding
| dc.creator | Brutti, Pierpaolo | |
| dc.date | 2008-01-22 | |
| dc.date.accessioned | 2026-07-07T08:55:48Z | |
| dc.date.available | 2026-07-07T08:55:48Z | |
| dc.description | Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+ε$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of $L^2([0,1],G_X)$ norm where $G_X(\cdot)$ denotes the (known) marginal distribution of the design variable $X$. Recently much work has been devoted to the construction of estimators that adapts in this setting (see, for example, [5,24,25,32]), but only a few of them come along with a easy--to--implement computational scheme. Here we propose a family of estimators based on the warped wavelet basis recently introduced by Picard and Kerkyacharian [36] and a tree-like thresholding rule that takes into account the hierarchical (across-scale) structure of the wavelet coefficients. We show that, if the regression function belongs to a certain class of approximation spaces defined in terms of $G_X(\cdot)$, then our procedure is adaptive and converge to the true regression function with an optimal rate. The results are stated in terms of excess probabilities as in [19]. | |
| dc.description | Submitted to 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/0801.3319 | |
| dc.identifier | http://arxiv.org/abs/0801.3319 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146390 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G07, 60K35 (Primary); 62G20 (Secondary) | |
| dc.title | Warped Wavelet and Vertical Thresholding | |
| dc.type | text |