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 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.b160139Published online 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 $0 Keywords : Berry-Esseen bound, recursive kernel estimator,$\alpha\$-mixing MSC numbers : 62G07, 62G20 Downloads: Full-text PDF