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

Fabienne Comte; Florence Merlevède

ESAIM: Probability and Statistics (2002)

- Volume: 6, page 211-238
- ISSN: 1292-8100

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topComte, Fabienne, and Merlevède, Florence. "Adaptive estimation of the stationary density of discrete and continuous time mixing processes." ESAIM: Probability and Statistics 6 (2002): 211-238. <http://eudml.org/doc/244680>.

@article{Comte2002,

abstract = {In this paper, we study the problem of non parametric estimation of the stationary marginal density $f$ of an $\alpha $ or a $\beta $-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 of a penalized contrast. We state non asymptotic risk bounds, regarding to the integrated quadratic risk, for our estimators, in both cases of mixing. We show that they are adaptive in the minimax sense over a large class of Besov balls. In discrete time, we also provide a result for model selection among an exponentially large collection of models (non regular case).},

author = {Comte, Fabienne, Merlevède, Florence},

journal = {ESAIM: Probability and Statistics},

keywords = {non parametric estimation; projection estimator; adaptive estimation; model selection; mixing processes; continuous time; discrete time},

language = {eng},

pages = {211-238},

publisher = {EDP-Sciences},

title = {Adaptive estimation of the stationary density of discrete and continuous time mixing processes},

url = {http://eudml.org/doc/244680},

volume = {6},

year = {2002},

}

TY - JOUR

AU - Comte, Fabienne

AU - Merlevède, Florence

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

JO - ESAIM: Probability and Statistics

PY - 2002

PB - EDP-Sciences

VL - 6

SP - 211

EP - 238

AB - In this paper, we study the problem of non parametric estimation of the stationary marginal density $f$ of an $\alpha $ or a $\beta $-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 of a penalized contrast. We state non asymptotic risk bounds, regarding to the integrated quadratic risk, for our estimators, in both cases of mixing. We show that they are adaptive in the minimax sense over a large class of Besov balls. In discrete time, we also provide a result for model selection among an exponentially large collection of models (non regular case).

LA - eng

KW - non parametric estimation; projection estimator; adaptive estimation; model selection; mixing processes; continuous time; discrete time

UR - http://eudml.org/doc/244680

ER -

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