Author
Listed:
- Ganggang Xu
- Jingfei Zhang
- Yehua Li
- Yongtao Guan
Abstract
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 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. Supplementary materials for this article are available online.
Suggested Citation
Ganggang Xu & Jingfei Zhang & Yehua Li & Yongtao Guan, 2024.
"Bias-Correction and Test for Mark-Point Dependence with Replicated Marked Point Processes,"
Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 217-231, January.
Handle:
RePEc:taf:jnlasa:v:119:y:2024:i:545:p:217-231
DOI: 10.1080/01621459.2022.2106234
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