科学研究

Professor Yongtao Guan received his PhD in Statistics from Texas A&M University in 2003. He was Assistant Professor of Management Science at the University of Miami from 2003 to 2006, Assistant/Associate Professor of Biostatistics at Yale University from 2006 to 2011, and Professor of Management Science at the University of Miami from 2011 to 2023. He served as the Chair of the Department of Management Science at the University of Miami from 2013 to 2020. He is currently Presidential Chair Professor in the School of Data Science at the Chinese University of Hong Kong, Shenzhen. He is a fellow of the American Statistical Association. His main research area is in spatio-temporal statistics. He has published extensively in leading statistical journals.

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 some real data examples.