A0580
Title: Bias-correction and test for mark-point dependence with replicated marked point processes
Authors: Yongtao Guan - Chinese University of Hong Kong, Shenzhen (China) [presenting]
Abstract: Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked-point processes. The focus is on adjusting for mark-point dependence when estimating the mean and covariance functions of the marking process, given independent replicates of the marked-point process. It is assumed 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. It is shown that this bias can be corrected using a local linear estimator of the cross-covariance function, and uniform convergence rates are established for the bias-corrected estimators. Furthermore, a test statistic based on local linear estimators for mark-point independence is proposed, and it 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.
