Central limit theorem for a class of random measures associated with germ-grain models
Central limit theorem for a class of random measures associated with germ-grain models
复制标题
与胚粒模型相关的一类随机测量的中心极限定理
DOI：
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复制
发表时间：
1996
影响因子：
1.2
通讯作者：
I. Molchanov
中科院分区：
文献类型：
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作者：
L. Heinrich;I. Molchanov
芽-粒模型定义为点过程的点（芽）移位的独立同分布的紧随机集（粒）的并集。本文引入了一类由胚粒模型产生的随机变量的平稳随机测度族，定义为单个粒子的非重叠部分的贡献之和。本文的主要结果是这些随机措施的中心极限定理，这适用于相当一般的独立标记的芽-粒模型，包括那些与非泊松分布的芽和非凸颗粒。它表明，这种随机测度的建设，包括那些随机措施所获得的积极扩展的固有体积。在泊松情形下，可以在较弱的假设下通过使用m-相依随机场的近似来证明中心极限定理。布尔模型的统计应用也进行了讨论。它们包括一个标准的方法来推导模型参数估计的极限定理。
The germ-grain model is defined as the union of independent identically distributed compact random sets (grains) shifted by points (germs) of a point process. The paper introduces a family of stationary random measures in ℝ d generated by germ-grain models and defined by the sum of contributions of non-overlapping parts of the individual grains. The main result of the paper is the central limit theorem for these random measures, which holds for rather general independently marked germ-grain models, including those with non-Poisson distribution of germs and non-convex grains. It is shown that this construction of random measures includes those random measures obtained by positively extended intrinsic volumes. In the Poisson case it is possible to prove a central limit theorem under weaker assumptions by using approximations by m-dependent random fields. Applications to statistics of the Boolean model are also discussed. They include a standard way to derive limit theorems for estimators of the model parameters.