Functional Estimation of a Density Under a New Weak Dependence Condition

Paul Doukhan and Sana Louhichi

Scandinavian Journal of Statistics, 2001, vol. 28, issue 2, 325-341

Abstract: 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 (cf. Doukhan & Louhichi, 1999) has sufficiently sharp properties to be used in various situations. More precisely we investigate the asymptotics of high order losses, asymptotic distributions and uniform almost sure behaviour of kernel density estimates. We prove that they are the same as for independent samples (with some restrictions for a.s. behaviours). Recall finally that this weak dependence condition extends on the previously defined ones such as mixing, association and it allows considerations of new classes such as weak shifts processes based on independent sequences as well as some non‐mixing Markov processes.

Date: 2001
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