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Adaptive estimation of the transition density of a Markov chain. (English) Zbl 1125.62087

Summary: A new estimator for the transition density \(\pi\) of a homogeneous Markov chain is considered. We introduce an original contrast derived from a 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 \(B^{(\alpha 1,\alpha 2)}_{2,\infty}\). Some simulations are also presented.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
62G05 Nonparametric estimation
62H12 Estimation in multivariate analysis
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