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Activity Number: 421 - Recent Advances in Time Series and Temporal Data Analysis
Type: Invited
Date/Time: Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
Sponsor: Business and Economic Statistics Section
Abstract #308087
Title: Semiparametric Modeling of Structured Point Processes Using Multi-Level Log-Gaussian Cox Processes
Author(s): Yongtao Guan*
Companies: University of Miami
Keywords: point process; functional data

We propose a general framework of using multi-level log-Gaussian Cox processes to model repeatedly observed point processes with complex structures. A novel nonparametric approach is developed to consistently estimate the covariance kernels of the latent Gaussian processes at all levels. Consequently, multi-level functional principal component analysis can be conducted to investigate the various sources of variations in the observed point patterns. In particular, to predict the functional principal component scores, we propose a consistent estimation procedure by maximizing the conditional likelihoods of super-positions of point processes. We further extend our procedure to the bivariate point process case where potential correlations between the processes can be assessed. Asymptotic properties of the proposed estimators are investigated, and the effectiveness of our procedures is illustrated by a simulation study and an application to a stock trading dataset.

Authors who are presenting talks have a * after their name.

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