TY - JOUR
T1 - Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samples
AU - Xing, Guo Dong
AU - Yang, Shan Chao
AU - Li, Xiaohu
N1 - Publisher Copyright:
© 2017, © 2017 Taylor & Francis Group, LLC.
PY - 2019/2/7
Y1 - 2019/2/7
N2 - In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n − 1/11 ) under the given conditions.
AB - In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n − 1/11 ) under the given conditions.
KW - Berry-Esseen bound
KW - Frequency polygons
KW - Uniformly Strong consistency
KW - α-mixing
UR - http://www.scopus.com/inward/record.url?scp=85032223372&partnerID=8YFLogxK
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U2 - 10.1080/03610918.2017.1381741
DO - 10.1080/03610918.2017.1381741
M3 - Article
AN - SCOPUS:85032223372
SN - 0361-0918
VL - 48
SP - 416
EP - 430
JO - Communications in Statistics: Simulation and Computation
JF - Communications in Statistics: Simulation and Computation
IS - 2
ER -