Frequency polygons for continuous random fields

被引：4
作者：
Bensaïd N. [1 ]
Dabo-Niang S. [1 ]
机构：
[1] Laboratoire EQUIPPE, Université Charles De Gaulle, Lille 3, 59653 Villeneuve d'Ascq Cedex, maison de la recherche,domaine du pont de bois
来源：
Statistical Inference for Stochastic Processes | 2010年 / 13卷 / 1期
关键词：
Density estimation; Frequency polygons; Mixing sample; Random field; Spatial data;
D O I：
10.1007/s11203-009-9038-7
中图分类号：
学科分类号：
摘要：
We study the frequency polygon investigated by Scott (J Am Stat Assoc 80: 348-354, 1985) as a nonparametric density estimate for a continuous and stationary real random field (Xt,tεℝN). We establish the asymptotic expressions for the integrated pointwise squared bias and the integrated pointwise squared variance of the estimate when the field is observed over a rectangular domain of ℝN. Under mild mixing conditions, we show that the estimate achieves the same rate of convergence to zero of the integrated mean squared error as kernel estimators and it can also attain the optimal uniform strong rate of convergence, for appropriate choices of the bin widths. © Springer Science+Business Media B.V. 2009.
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页码：55 / 80
页数：25
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