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The Rate of Asymptotic Normality of Frequency Polygon Density Estimation for Spatial Random Fields
School of Mathematics and Statistics, Guangxi Normal University, Guilin, China
Department of Mathematics, Guilin University of Aerospace Technology, Guilin, China
School of Mathematical Sciences, Xiamen University, Xiamen, China
School of Mathematics, Shangrao Normal University, Shangrao, China
- 1 School of Mathematics and Statistics, Guangxi Normal University, Guilin, China
- 2 Department of Mathematics, Guilin University of Aerospace Technology, Guilin, China
- 3 School of Mathematical Sciences, Xiamen University, Xiamen, China
- 4 School of Mathematics, Shangrao Normal University, Shangrao, China
Open Journal of Statistics·Volume 08 (2018)·Pages 962–973·Published 14 November 2018·DOI10.4236/ojs.2018.86064
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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.
KeywordsFrequency PolygonBerry-Esseen BoundRate of Asymptotic NormalityMixing Random Field
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