arXiv subjects

Claire Lacour

Publications and source records attributed to Claire Lacour.

21 records · Page 2Linked to original sources

arXiv2006

Adaptive estimation of the transition density of a Markov chain

In this paper a new estimator for the transition density $π$ 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 $π$ under mild conditions. The resulting estimate is adaptive with an optimal rate of convergence over a large range of anisotropic Besov spaces $B_{2,\infty}^{(α_1,α_2)}$. Some simulations are also presented.

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arXiv2006

Rates of convergence for nonparametric deconvolution

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators.

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arXiv2006

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

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.

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