Rates of convergence for minimal distances in the central limit theorem under projective criteria.
Recent advances in invariance principles for stationary sequences.
Adaptive estimation of the stationary density of discrete and continuous time mixing processes
In this paper, we study the problem of non parametric estimation of the stationary marginal density of an or a -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed via the minimization...
Adaptive estimation of the stationary density of discrete and continuous time mixing processes
In this paper, we study the problem of non parametric estimation of the stationary marginal density of an or a -mixing process, observed either in continuous time or in discrete time. We present an unified framework allowing to deal with many different cases. We consider a collection of finite dimensional linear regular spaces. We estimate using a projection estimator built on a data driven selected linear space among the collection. This data driven choice is performed the minimization of...
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Considering the centered empirical distribution function as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.
A quenched weak invariance principle
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
Moderate deviations for stationary sequences of bounded random variables
In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.
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