论文标题
在滋扰协变量存在下，空间点模式的协变量显着性的非参数测试
Nonparametric testing of the covariate significance for spatial point patterns under the presence of nuisance covariates
论文作者
论文摘要
确定相关的空间协变量是分析点模式分析中最重要的问题之一。参数方法可能会导致不正确的结论，尤其是当点之间的相互作用模型是错误的。因此，我们提出了一种完全非参数的方法来测试协变量的重要性，并考虑到滋扰协变量的可能影响。我们的测试与名义显着性水平相匹配，并且在强度函数模型和相互作用模型都正确的情况下，它们的功能与参数测试的功能相当。当强度函数的参数模型是错误的时，我们的测试实现了更高的功能。所提出的方法依赖于蒙特卡洛测试并利用新引入的协变量加权残余度量。我们还定义了点过程与协变量与部分相关系数之间的相关系数，从而量化了点过程与感兴趣的协变量之间的依赖性，同时消除了滋扰协变量的影响。
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong. Therefore, we propose a fully nonparametric approach to testing significance of a covariate, taking into account the possible effects of nuisance covariates. Our tests match the nominal significance level, and their powers are comparable with the powers of parametric tests in cases where both the model for intensity function and the model for interactions are correct. When the parametric model for the intensity function is wrong, our tests achieve higher powers. The proposed methods rely on Monte Carlo testing and take advantage of the newly introduced covariate-weighted residual measure. We also define a correlation coefficient between a point process and a covariate and a partial correlation coefficient quantifying the dependence between a point process and a covariate of interest while removing the influence of nuisance covariates.
