Recursive kernel estimation of the density under η-weak dependence

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 α-mixing sequences. In this work, we are interested in η-weak dependence, which is different from the notion of α-mixing. We provide the variance and the mean squared error of this estimator. The asymptotic normality is also discussed. A simulation study for two η-dependent models which are not necessarily α-mixing shows the advantage in time computation of considering the recursive kernel estimation rather than the Parzen-Rosenblatt one.