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Functional Estimation of a Density Under a New Weak Dependence Condition
Author(s) -
Doukhan Paul,
Louhichi Sana
Publication year - 2001
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00240
Subject(s) - mathematics , mixing (physics) , estimator , kernel density estimation , statistical physics , kernel (algebra) , density estimation , markov chain , weak convergence , pure mathematics , statistics , physics , computer security , quantum mechanics , computer science , asset (computer security)
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.