Sparse estimation for generalized exponential marked Hawkes process

TL;DR

This paper introduces a sparse estimation technique for the generalized exponential marked Hawkes process using penalized likelihood, providing theoretical analysis and numerical validation for variable selection accuracy.

Contribution

It develops a novel penalized estimation framework for the generalized exponential marked Hawkes process, addressing nuisance parameters and boundary issues.

Findings

The method effectively selects relevant variables in simulated examples.

Theoretical probability bounds for correct variable selection are established.

Numerical simulations demonstrate the method's practical performance.

Abstract

We have established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to the ordinary method (P-O) estimator. Furthermore, we evaluated the probability of correct variable selection. In order to achieve this, we established a framework for a likelihood analysis and the P-O estimation when there might be nuisance parameters and the true value of the parameter could be realized at the boundary of the parameter space. Numerical simulations are given for several important examples.