# Adaptive estimation of the transition density of a Markov chain

Abstract : In this paper a new estimator for the transition density $\pi$ of an homogeneous Markov chain is considered. We introduce an original contrast derived from regression framework and we use a model selection method to estimate $\pi$ under mild conditions. The resulting estimate is adaptive with an optimal rate of convergence over a large range of anisotropic Besov spaces $B_{2,\infty}^{(\alpha_1,\alpha_2)}$. Some simulations are also presented.
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Submitted on : Wednesday, November 22, 2006 - 11:44:39 AM
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Claire Lacour. Adaptive estimation of the transition density of a Markov chain. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institut Henri Poincaré (IHP), 2007, 43 (5), pp.571-597. ⟨10.1016/j.anihpb.2006.09.003⟩. ⟨hal-00115617⟩

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