%0 Journal Article
%T The Rate of Asymptotic Normality of Frequency Polygon Density Estimation for Spatial Random Fields
%A Shanchao Yang
%A Xin Yang
%A Guodong Xing
%A Yongming Li
%J Open Journal of Statistics
%P 962-973
%@ 2161-7198
%D 2018
%I Scientific Research Publishing
%R 10.4236/ojs.2018.86064
%X 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</span></span><span><span><span> <img src=\"Edit_53607847-ca4a-4dac-8ac1-54a3a3883538.bmp\" alt=\"\" /></span></span></span><span><span><span style=\"font-family:&quot;\">, it is showed that the convergence rate of
asymptotic normality reaches to</span></span></span><span><span><span style=\"font-family:&quot;\"> <img src=\"Edit_873777a9-6fcc-4bf1-a9d3-386377ebd6a2.bmp\" alt=\"\" /></span></span></span><span><span><span style=\"font-family:&quot;\">&nbsp;when
mixing coefficient tends to zero exponentially fast.
%K Frequency Polygon
%K Berry-Esseen Bound
%K Rate of Asymptotic Normality
%K Mixing Random Field
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=89596