TITLE:
The Rate of Asymptotic Normality of Frequency Polygon Density Estimation for Spatial Random Fields
AUTHORS:
Shanchao Yang, Xin Yang, Guodong Xing, Yongming Li
KEYWORDS:
Frequency Polygon, Berry-Esseen Bound, Rate of Asymptotic Normality, Mixing Random Field
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.6,
December
29,
2018
ABSTRACT: This
paper is to investigate the convergence rate of asymptotic normality of
frequency polygon estimation for density function under mixing random fields,
which include strongly mixing condition and some weaker mixing conditions. A
Berry-Esseen bound of frequency polygon is established and the convergence
rates of asymptotic normality are derived. In particularly, for the optimal bin
width , it is showed that the convergence rate of
asymptotic normality reaches to when
mixing coefficient tends to zero exponentially fast.