非参数统计
估计员
参数统计
点过程
一致性(知识库)
拟合优度
蒙特卡罗方法
功能(生物学)
统计假设检验
数学
参数化模型
计算机科学
统计
算法
人工智能
进化生物学
生物
作者
Ganggang Xu,Liang Chen,Rasmus Waagepetersen,Yongtao Guan
标识
DOI:10.1080/01621459.2022.2029456
摘要
Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte Carlo tests. The proposed tests crucially rely on accurate nonparametric estimation of the second-order properties of a point process. To address this we propose a new nonparametric pair correlation function (PCF) estimator for clustered spatial point processes under some mild shape constraints, which is shown to achieve uniform consistency. The proposed test statistics are computationally efficient owing to closed-form asymptotic distributions and achieve the nominal size even for testing composite hypotheses. In practice, the proposed estimation and testing procedures provide effective tools to improve parametric intensity function modeling, which is demonstrated through extensive simulation studies as well as a real data analysis of street crime activity in Washington DC. Supplementary materials for this article are available online.
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