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Adaptive estimation of the stationary density of discrete and continuous time mixing processes

Fabienne Comte;  Florence Merlevède — 2002

ESAIM: Probability and Statistics

In this paper, we study the problem of non parametric estimation of the stationary marginal density f of an α or a β -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 f 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

Fabienne Comte;  Florence Merlevède — 2010

ESAIM: Probability and Statistics

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...

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