Deconvolution for an atomic distribution
| dc.creator | van Es, Bert | |
| dc.creator | Gugushvili, Shota | |
| dc.creator | Spreij, Peter | |
| dc.date | 2007-09-21 | |
| dc.date | 2008-04-30 | |
| dc.date.accessioned | 2026-07-07T09:35:42Z | |
| dc.date.available | 2026-07-07T09:35:42Z | |
| dc.description | Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+σZ_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli distribution with probability of zero equal to $p$ and $V$ has a distribution function $F$ with density $f.$ Furthermore, let the random variables $Z_i$ have the standard normal distribution and let $σ>0.$ Based on a sample $X_1,..., X_n,$ we consider the problem of estimation of the density $f$ and the probability $p.$ We propose a kernel type deconvolution estimator for $f$ and derive its asymptotic normality at a fixed point. A consistent estimator for $p$ is given as well. Our results demonstrate that our estimator behaves very much like the kernel type deconvolution estimator in the classical deconvolution problem. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-EJS121 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/0709.3413 | |
| dc.identifier | http://arxiv.org/abs/0709.3413 | |
| dc.identifier | Electronic Journal of Statistics 2008, Vol. 2, 265-297 | |
| dc.identifier | doi:10.1214/07-EJS121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159918 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G07 (Primary) 62G20 (Secondary) | |
| dc.title | Deconvolution for an atomic distribution | |
| dc.type | text |