Bias-Correction and Test for Mark-Point Dependence with Replicated Marked Point Processes

• 成果类型: Article
• 署名作者: Xu, Ganggang; Zhang, Jingfei; Li, Yehua; Guan, Yongtao
• 署名单位: University of Miami; University of California System; University of California Riverside
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2106234
• 发表日期: 2024
• 页码: 217-231
• 关键词: functional data-analysis; smoking; INDEPENDENCE; regression; SPARSE

摘要

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 root 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. for this article are available online.