## Electronic Journal of Statistics

### Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process

#### Abstract

We consider the task of learning the structure of the graph underlying a mutually-exciting multivariate Hawkes process in the high-dimensional setting. We propose a simple and computationally inexpensive edge screening approach. Under a subset of the assumptions required for penalized estimation approaches to recover the graph, this edge screening approach has the sure screening property: with high probability, the screened edge set is a superset of the true edge set. Furthermore, the screened edge set is relatively small. We illustrate the performance of this new edge screening approach in simulation studies.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 1207-1234.

Dates
First available in Project Euclid: 11 April 2017

https://projecteuclid.org/euclid.ejs/1491897620

Digital Object Identifier
doi:10.1214/17-EJS1251

Mathematical Reviews number (MathSciNet)
MR3634334

Zentralblatt MATH identifier
1364.60061

#### Citation

Chen, Shizhe; Witten, Daniela; Shojaie, Ali. Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process. Electron. J. Statist. 11 (2017), no. 1, 1207--1234. doi:10.1214/17-EJS1251. https://projecteuclid.org/euclid.ejs/1491897620

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