Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes
Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes
复制标题
经验二阶乘积密度积分平方误差的中心极限定理和驻点过程的拟合优度检验
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Stella Klein
中科院分区：
文献类型：
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作者：
L. Heinrich;Stella Klein
空间点过程是d维空间中不规则或随机点模式的数学模型，在实际应用中，通常d = 2或d = 3。二阶乘积密度及其各向同性的类似物对相关函数是分析平稳点过程的重要工具。在目前的工作中，我们推导出中心极限定理的经验二阶产品密度的集成平方误差（伊势）和经验对相关函数的伊势时，观察窗口无限扩大。证明技术是基于高阶累积量措施和Brillinger混合属性的基础点过程。所得到的高斯极限被用来构造渐近拟合优度检验检查点过程假设，即使在非泊松的情况下。
Abstract Spatial point processes are mathematical models for irregular or random point patterns in the d-dimensional space, where usually d = 2 or d = 3 in applications. The second-order product density and its isotropic analogue, the pair correlation function, are important tools for analyzing stationary point processes. In the present work we derive central limit theorems for the integrated squared error (ISE) of the empirical second-order product density and for the ISE of the empirical pair correlation function when the observation window expands unboundedly. The proof techniques are based on higher-order cumulant measures and the Brillinger-mixing property of the underlying point processes. The obtained Gaussian limits are used to construct asymptotic goodness-of-fit tests for checking point process hypotheses even in the non-Poissonian case.