Adaptivity in convolution models with partially known noise distribution
| dc.creator | Butucea, Cristina | |
| dc.creator | Matias, Catherine | |
| dc.creator | Pouet, Christophe | |
| dc.date | 2008-04-07 | |
| dc.date | 2008-10-03 | |
| dc.date.accessioned | 2026-07-07T10:06:57Z | |
| dc.date.available | 2026-07-07T10:06:57Z | |
| dc.description | We consider a semiparametric convolution model. We observe random variables having a distribution given by the convolution of some unknown density $f$ and some partially known noise density $g$. In this work, $g$ is assumed exponentially smooth with stable law having unknown self-similarity index $s$. In order to ensure identifiability of the model, we restrict our attention to polynomially smooth, Sobolev-type densities $f$, with smoothness parameter $β$. In this context, we first provide a consistent estimation procedure for $s$. This estimator is then plugged-into three different procedures: estimation of the unknown density $f$, of the functional $\int f^2$ and goodness-of-fit test of the hypothesis $H_0:f=f_0$, where the alternative $H_1$ is expressed with respect to $\mathbb {L}_2$-norm (i.e. has the form $ψ_n^{-2}\|f-f_0\|_2^2\ge \mathcal{C}$). These procedures are adaptive with respect to both $s$ and $β$ and attain the rates which are known optimal for known values of $s$ and $β$. As a by-product, when the noise density is known and exponentially smooth our testing procedure is optimal adaptive for testing Sobolev-type densities. The estimating procedure of $s$ is illustrated on synthetic data. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-EJS225 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/0804.1056 | |
| dc.identifier | http://arxiv.org/abs/0804.1056 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 897-915 | |
| dc.identifier | doi:10.1214/08-EJS225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170469 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62F12, 62G05 (Primary) 62G10, 62G20 (Secondary) | |
| dc.title | Adaptivity in convolution models with partially known noise distribution | |
| dc.type | text |