Lacour, Claire Adaptive estimation of the transition density of a Markov chain. (English) Zbl 1125.62087 Ann. Inst. Henri Poincaré, Probab. Stat. 43, No. 5, 571-597 (2007). 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. Cited in 16 Documents MSC: 62M05 Markov processes: estimation; hidden Markov models 62F12 Asymptotic properties of parametric estimators 62G05 Nonparametric estimation 62H12 Estimation in multivariate analysis Keywords:adaptive estimation; transition density; Markov chain; model selection; penalized contrast PDFBibTeX XMLCite \textit{C. Lacour}, Ann. Inst. Henri Poincaré, Probab. Stat. 43, No. 5, 571--597 (2007; Zbl 1125.62087) Full Text: DOI arXiv Numdam Numdam EuDML