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Article Dans Une Revue Journal of Multivariate Analysis Année : 2008

Adaptive estimation of the transition density of a particular hidden Markov chain

Claire Lacour

Résumé

We study the following model of hidden Markov chain: $Y_i=X_i+\varepsilon_i$, $ i=1,\dots,n+1$ with $(X_i)$ a real-valued positive recurrent and stationary Markov chain and $(\varepsilon_i)_{1\leq i\leq n+1}$ 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.
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Dates et versions

hal-00115612 , version 1 (22-11-2006)

Identifiants

Citer

Claire Lacour. Adaptive estimation of the transition density of a particular hidden Markov chain. Journal of Multivariate Analysis, 2008, 99 (5), pp.787-814. ⟨10.1016/j.jmva.2007.04.006⟩. ⟨hal-00115612⟩
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