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Functional estimation of a density under a weak dependence condition. (Estimation de la densité d’une suite faiblement dépendante.) (French) Zbl 0919.62029

Summary: The purpose of this paper is to prove through the analysis of the behaviour of a standard kernel density estimator that the notion of weak dependence defined in a previous paper [the first author, Prépubl. 97.08, Univ. Paris-Sud (1997)] has sharp properties enough to be used in various situations. This weak dependence condition extends the previously defined ones such as mixing, association, and it allows to consider new classes such as weak shift processes based on independent sequences as well as some non-mixing Markov processes.

MSC:

62G07 Density estimation
62M99 Inference from stochastic processes
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