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Recursive kernel estimation of the density under η-weak dependence
Kenza Assia Mezhoud,Zaher Mohdeb,Sana Louhichi 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.3
The purpose of this paper is to study the asymptotic behaviour of the recursive kerneldensity estimator. This estimator was introduced and investigated by Amiri (2010)for independent and α-mixing sequences. In this work, we are interested in η-weakdependence, which is different from the notion of α-mixing. We provide the variance andthe mean squared error of this estimator. The asymptotic normality is also discussed. Asimulation study for two η-dependent models which are not necessarily α-mixing showsthe advantage in time computation of considering the recursive kernel estimation ratherthan the Parzen–Rosenblatt one.