Sparse estimation for generalized exponential marked Hawkes process

Springer Science and Business Media LLC - Tập 26 - Trang 139-169 - 2022
Masatoshi Goda1,2
1Graduate School of Mathematical Sciences, University of Tokyo, Tokyo, Japan
2Japan Science and Technology, CREST, Saitama, Japan

Tóm tắt

We established a sparse estimation method for the generalized exponential marked Hawkes process by the penalized method to ordinary method (P–O) estimator. Furthermore, we evaluated the probability of the correct variable selection. In the course of 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 might be at the boundary of the parameter space. Finally, numerical simulations are given for several important examples.

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