Recursive kernel estimation of the density under eta-weak dependence

Kenza Assia (1) , Zaher Mohdeb (1) , Sana Louhichi (2)

1 Université de Constantine
2 IPS - Inférence Processus Stochastiques

The purpose of this paper is to study the asymptotic behaviour of the recursive kernel density estimator. This estimator was introduced and investigated by Amiri (2010) for independent and alpha-mixing sequences. In this work, we are interested in eta-weak dependence, which is different from the notion of alpha-mixing. We provide the variance and the mean squared error of this estimator. The asymptotic normality is also discussed. A simulation study for two eta-dependent models which are not necessarily alpha-mixing shows the advantage in time computation of considering the recursive kernel estimation rather than the Parzen–Rosenblatt one.

Domaines: Statistiques [math.ST]

Kenza Assia, Zaher Mohdeb, Sana Louhichi. Recursive kernel estimation of the density under eta-weak dependence. Journal of the Korean Statistical Society, 2014, 43 (3), pp.403-414. ⟨10.1016/j.jkss.2013.12.003⟩. ⟨hal-01892336⟩