论文标题
偏置校正和测试标记点依赖性，并具有重复的标记点过程
Bias-correction and Test for Mark-point Dependence with Replicated Marked Point Processes
论文作者
论文摘要
标记点依赖性在研究问题中起着至关重要的作用，这些问题可以安装在标记过程的一般框架中。在这项工作中，在给定标记点过程的独立复制时，我们专注于在估计标记过程的平均值和协方差函数时调整标记点依赖性。我们假设标记过程是一个高斯过程，并且点过程是一个对数高斯的COX过程，其中标记点依赖性是通过两个潜在高斯过程之间的依赖性生成的。在此框架下，忽略标记点依赖性的天真局部线性估计器可能会严重偏差。我们表明，可以使用跨互相函数的局部线性估计器来纠正这种偏差，并建立偏置校正估计器的均匀收敛速率。此外，我们提出了一个基于标记点独立性的局部线性估计器的测试统计量，该测试量估计量被证明会收敛到参数$ \ sqrt {n} $ - 收敛速率中的渐近正态分布。为关键模型假设开发了模型诊断工具，并为更一般的标记点过程提出了强大的功能置换测试。使用大量的模拟和应用程序对两个真实数据示例进行了广泛的模拟和应用，证明了所提出方法的有效性。
Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance functions of the mark process, given independent replicates of the marked point process. We assume that the mark process is a Gaussian process and the point process is a log-Gaussian Cox process, where the mark-point dependence is generated through the dependence between two latent Gaussian processes. Under this framework, naive local linear estimators ignoring the mark-point dependence can be severely biased. We show that this bias can be corrected using a local linear estimator of the cross-covariance function and establish uniform convergence rates of the bias-corrected estimators. Furthermore, we propose a test statistic based on local linear estimators for mark-point independence, which is shown to converge to an asymptotic normal distribution in a parametric $\sqrt{n}$-convergence rate. Model diagnostics tools are developed for key model assumptions and a robust functional permutation test is proposed for a more general class of mark-point processes. The effectiveness of the proposed methods is demonstrated using extensive simulations and applications to two real data examples.
