Claire Lacour

Rates of convergence for nonparametric deconvolution

Abstract 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. To cite this article: C. Lacour, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

Adaptive estimation of the transition density of a Markov chain

Abstract 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 , ∞ ( α 1 , α 2 ) . Some simulations are also presented.

Nonparametric estimation of the stationary density and the transition density of a Markov chain

In this paper, we study first the problem of nonparametric estimation of the stationary density f of a discrete-time Markov chain (Xi). We consider a collection of projection estimators on finite dimensional linear spaces. We select an estimator among the collection by minimizing a penalized contrast. The same technique enables us to estimate the density g of (Xi,Xi+1) and so to provide an adaptive estimator of the transition density [pi]=g/f. We give bounds in L2 norm for these estimators and we show that they are adaptive in the minimax sense over a large class of Besov spaces. Some examples and simulations are also provided.

Inhomogeneous and anisotropic conditional density estimation from dependent data

The problem of estimating a conditional density is considered. Given a collection of partitions, we propose a procedure that selects from the data the best partition among that collection and then provides the best piecewise polynomial estimator built on that partition. The observations are not supposed to be independent but only

Adaptive pointwise estimation of conditional density function

\beta

Estimator selection: a new method with applications to kernel density estimation

-mixing; in particular, our study includes the estimation of the transition density of a Markov chain. For a well-chosen collection of possibly irregular partitions, we obtain oracle-type inequalities and adaptivity results in the minimax sense over a wide range of possibly anisotropic and inhomogeneous Besov classes. We end with a short simulation study.

Least squares type estimation of the transition density of a particular hidden Markov chain

In this paper we consider the problem of estimating

Data‐driven density estimation in the presence of additive noise with unknown distribution

f

Anisotropic adaptive kernel deconvolution

, the conditional density of

Data driven density estimation in presence of unknown convolution operator

Y