Berry-Esseen bounds of recursive kernel estimator of density under strong mixing assumptions
Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 343-358 https://doi.org/10.4134/BKMS.b160139 Published online November 3, 2016 Printed January 31, 2017
Yu-Xiao Liu and Si-Li Niu Henan University of Urban Construction, Tongji University
Abstract : Let $\{X_i\}$ be a sequence of stationary $\a$-mixing random variables with probability density function $f(x)$. The recursive kernel estimators of $f(x)$ are defined by $$ \widehat{f}_n(x)=\frac{1}{n\sqrt{b_n}}\sum^n_{j=1}b_j^{-\frac{1}{2}}K\Big(\frac{x-X_j}{b_j}\Big)~~\mbox{and}~~ \widetilde{f}_n(x)=\frac{1}{n}\sum^n_{j=1}\frac{1}{b_j}K\Big(\frac{x-X_j}{b_j}\Big), $$ where $0
