Author(s)

Shanchao Yang¹, Xin Yang^2*, Guodong Xing³, Yongming Li⁴

¹School of Mathematics and Statistics, Guangxi Normal University, Guilin, China.
²Department of Mathematics, Guilin University of Aerospace Technology, Guilin, China.
³School of Mathematical Sciences, Xiamen University, Xiamen, China.
⁴School of Mathematics, Shangrao Normal University, Shangrao, China.

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.

Frequency Polygon, Berry-Esseen Bound, Rate of Asymptotic Normality, Mixing Random Field

Yang, S. , Yang, X. , Xing, G. and Li, Y. (2018) The Rate of Asymptotic Normality of Frequency Polygon Density Estimation for Spatial Random Fields. Open Journal of Statistics, 8, 962-973. doi: 10.4236/ojs.2018.86064.