Nonparametric Testing of Distribution Functions in Germ-grain Models
Nonparametric Testing of Distribution Functions in Germ-grain Models
复制标题
种粒模型中分布函数的非参数检验
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
L. Heinrich
中科院分区：
文献类型：
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作者：
Z. Pawlas;L. Heinrich
胚粒模型是d维欧氏空间中的随机闭集，它允许表示为随机紧集（称为颗粒）被点过程的原子（称为胚）移动的并集。本文研究了一个m维随机向量的分布函数F，该随机向量描述了一个稳态胚粒模型中典型颗粒的形状和尺寸参数。本文提出了一个比率无偏加权（Horvitz-Thompson型）经验分布函数（hat F_n），它是根据完全位于取样窗口W_n内的移动颗粒的相应数据向量来估计F的。由于随着Wn的增加，经验过程（hat F_n）（t）− F（t）（标度后）弱收敛于m参数布朗桥过程，因此在m = 1的特殊情况下，可以检验观测数据对假设的连续分布函数F的拟合优度，类似于Kolmogorov-Smirnov检验。
Germ-grain models are random closed sets in the d-dimensional Euclidean space ℝd which admit a representation as union of random compact sets (called grains) shifted by the atoms (called germs) of a point process. In this note we consider the distribution function F of an m-dimensional random vector describing shape and size parameters of the typical grain of a stationary germ-grain model. We suggest a ratio-unbiased weighted (Horvitz-Thompson type) empirical distribution function (hat F_n ) to estimate F, based on the corresponding data vectors of those shifted grains which lie completely within the sampling window Wn ⊆ ℝd. Since, as Wn increases, the empirical process (hat F_n )(t) − F(t) (after scaling) converges weakly to an m-parameter Brownian bridge process, it is possible for the particular case where m = 1, to examine the the goodness-of-fit of observed data to a hypothesised continuous distribution function F, analogous to the Kolmogorov-Smirnov test.