Abstract

We propose a new method for analysis of multivariate point pattern data observed in a heterogeneous environment and with complex intensity functions. We suggest semiparametric models for the intensity functions that depend on an unspecified factor common to all types of points. This is for example well suited for analyzing spatial covariate effects on events such as street crime activities that occur in a complex urban environment. A multinomial conditional composite likelihood function is introduced for estimation of intensity function regression parameters and the asymptotic joint distribution of the resulting estimators is derived under mild conditions. Crucially, the asymptotic covariance matrix depends on ratios of cross pair correlation functions of the multivariate point process. To make valid statistical inference without restrictive assumptions, we construct consistent nonparametric estimators for these ratios. Finally, we construct standardized residual plots, predictive probability plots, and semiparametric intensity plots to validate and to visualize the findings of the model. The effectiveness of the proposed methodology is demonstrated through extensive simulation studies and an application to analyzing the effects of socio-economic and demographical variables on occurrences of street crimes in Washington DC. Supplementary materials for this article are available online.

摘要

我们提出了一种分析在异构环境中观察到的具有复杂强度函数的多变量点模式数据的新方法。我们建议强度函数的半参数模型取决于所有类型点共有的未指定因子。例如，这非常适合分析空间协变量对事件（例如复杂城市环境中发生的街头犯罪活动）的影响。引入多项条件复合似然函数来估计强度函数回归参数，并在温和条件下导出所得估计量的渐近联合分布。至关重要的是，渐近协方差矩阵取决于多元点过程的交叉对相关函数的比率。为了在没有限制性假设的情况下进行有效的统计推断，我们为这些比率构建了一致的非参数估计量。最后，我们构建标准化残差图、预测概率图和半参数强度图来验证和可视化模型的结果。通过广泛的模拟研究和应用分析社会经济和人口变量对华盛顿特区街头犯罪发生的影响，证明了所提出方法的有效性。本文的补充材料可在线获取。通过广泛的模拟研究和应用分析社会经济和人口变量对华盛顿特区街头犯罪发生的影响，证明了所提出方法的有效性。本文的补充材料可在线获取。通过广泛的模拟研究和应用分析社会经济和人口变量对华盛顿特区街头犯罪发生的影响，证明了所提出方法的有效性。本文的补充材料可在线获取。