Sharp optimality for density deconvolution with dominating bias
| dc.creator | Butucea, Cristina | |
| dc.creator | Tsybakov, Alexandre B. | |
| dc.date | 2004-09-24 | |
| dc.date.accessioned | 2026-07-07T08:06:28Z | |
| dc.date.available | 2026-07-07T08:06:28Z | |
| dc.description | We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a class $\mathcal{A}$ of densities whose characteristic function is described by the exponent $\exp(-α|u|^r)$ as $|u|\to \infty$, where $α>0$, $r>0$. The noise density is supposed to be known and such that its characteristic function decays as $\exp(-β|u|^s)$, as $|u| \to \infty$, where $β>0$, $s>0$. Assuming that $r<s$, we suggest a kernel type estimator that is optimal in sharp asymptotical minimax sense on $\mathcal{A}$ simultaneously under the pointwise and the $\mathbb{L}_2$-risks. The variance of the estimators turns out to be asymptotically negligible w.r.t. its squared bias. For $r<s/2$ we construct a sharp adaptive estimator of $f$. We discuss some effects of dominating bias, such as superefficiency of minimax estimators. | |
| dc.identifier | https://arxiv.org/abs/math/0409471 | |
| dc.identifier | http://arxiv.org/abs/math/0409471 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130619 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05, 62G20 | |
| dc.title | Sharp optimality for density deconvolution with dominating bias | |
| dc.type | text |