Statistical Estimation, Uncertainty Quantification, and Detection for Hawkes Processes
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Wang, Haoyun
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Abstract
Recently Hawkes process, also known as spatio-temporal self-exciting point process, has become popular for modeling event data. Its strength lies in its ability to capture complex dependencies between events, particularly the triggering effect, which is closely related to the concept of Granger causality in time series analysis. This thesis focus on the theoretical aspects of the statistical learning problem of such effect in the linear Hawkes process model in three chapters. The topics include (parametric) uncertainty quantification in a network setting, (parametric) quickest change-point detection, and estimation of triggering effect using a general kernel function which may in practice be represented by neural networks.
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2024-12-08
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Dissertation