Adaptive estimation of the transition density of a particular hidden Markov chain
| dc.creator | Lacour, Claire | |
| dc.date | 2006-11-22 | |
| dc.date.accessioned | 2026-07-07T09:28:41Z | |
| dc.date.available | 2026-07-07T09:28:41Z | |
| dc.description | We study the following model of hidden Markov chain: $Y_i=X_i+ε_i$, $ i=1,...,n+1$ with $(X_i)$ a real-valued positive recurrent and stationary Markov chain and $(ε_i)_{1\leq i\leq n+1}$ a noise independent of the sequence $(X_i)$ having a known distribution. We present an adaptive estimator of the transition density based on the quotient of a deconvolution estimator of the density of $X_i$ and an estimator of the density of $(X_i,X_{i+1})$. These estimators are obtained by contrast minimization and model selection. We evaluate the $L2$ risk and its rate of convergence for ordinary smooth and supersmooth noise with regard to ordinary smooth and supersmooth chains. Some examples are also detailed. | |
| dc.identifier | https://arxiv.org/abs/math/0611681 | |
| dc.identifier | http://arxiv.org/abs/math/0611681 | |
| dc.identifier | Journal of Multivariate Analysis 99, 5 (2008) 787-814 | |
| dc.identifier | doi:10.1016/j.jmva.2007.04.006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157514 | |
| dc.subject | Statistics Theory | |
| dc.title | Adaptive estimation of the transition density of a particular hidden Markov chain | |
| dc.type | text |