Asymptotic gaussianity of some estimators for reduced factorial moment measures and product densities of stationary poisson cluster processes
Asymptotic gaussianity of some estimators for reduced factorial moment measures and product densities of stationary poisson cluster processes
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一些估计量的渐近高斯性，用于减少阶乘矩测量和平稳泊松簇过程的乘积密度
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发表时间：
1988
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通讯作者：
L. Heinrich
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作者：
L. Heinrich
本文的主要目的是在基础点过程为正则无穷可分过程时，给出经验阶乘矩测度和核型乘积密度估计的某些极限定理，包括泛函极限定理.所需矩条件是极小的，它们是保证所考虑估计的有限方差所必需的.在平稳Poisson过程的特殊情况下，所得结果被用来构造函数λK（t）的拟合优度检验，0≤t≤T，λ K（t）表示围绕过程的典型点的半径为t的球面内的点的平均数。
The main purpose of this paper is to present cer~trai limit tileoreins including functional limit theorems for empirical factorial moment measures and kernel-type product density estimators when the underlying point process is a regular infinitely divisible one.The requied moment conditions are minimal, they are necessary to ensure finite variances of the estimators under consideration. In the special case of a stationary poisson process the obtained results are used to construct a goodness-of-fit test for the function λK(t), 0≤t≤T, denoting the mean number of points within a sphere with radius t around a typical point of the process.