Nonparametric estimation of the stationary density and the transition density of a Markov chain
| dc.creator | Lacour, Claire | |
| dc.date | 2006-11-21 | |
| dc.date | 2008-01-09 | |
| dc.date.accessioned | 2026-07-07T08:53:22Z | |
| dc.date.available | 2026-07-07T08:53:22Z | |
| dc.description | In this paper, we study first the problem of nonparametric estimation of the stationary density $f$ of a discrete-time Markov chain $(X_i)$. We consider a collection of projection estimators on finite dimensional linear spaces. We select an estimator among the collection by minimizing a penalized contrast. The same technique enables to estimate the density $g$ of $(X_i, X_{i+1})$ and so to provide an adaptive estimator of the transition density $π=g/f$. We give bounds in $L^2$ norm for these estimators and we show that they are adaptive in the minimax sense over a large class of Besov spaces. Some examples and simulations are also provided. | |
| dc.identifier | https://arxiv.org/abs/math/0611645 | |
| dc.identifier | http://arxiv.org/abs/math/0611645 | |
| dc.identifier | Stochastic Processes and their Applications 118, 2 (2008) pp 232-260 | |
| dc.identifier | doi:10.1016/j.spa.2007.04.013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145596 | |
| dc.subject | Statistics Theory | |
| dc.title | Nonparametric estimation of the stationary density and the transition density of a Markov chain | |
| dc.type | text |