## The Annals of Applied Statistics

### Estimating links of a network from time to event data

#### Abstract

In this paper we develop a statistical method for identifying links of a network from time to event data. This method models the hazard function of a node conditional on event time of other nodes, parameterizing the conditional hazard function with the links of the network. It then estimates the hazard function by maximizing a pseudo partial likelihood function with parameters subject to a user-specified penalty function and additional constraints. To make such estimation robust, it adopts a pre-specified risk control on the number of false discovered links by using the Stability Selection method. Simulation study shows that under this hybrid procedure, the number of false discovered links is tightly controlled while the true links are well recovered. We apply our method to estimate a political cohesion network that drives donation behavior of 146 firms from the data collected during the 2008 Taiwanese legislative election. The results show that firms affiliated with elite organizations or firms of monopoly are more likely to diffuse donation behavior. In contrast, firms belonging to technology industry are more likely to act independently on donation.

#### Article information

Source
Ann. Appl. Stat., Volume 11, Number 3 (2017), 1429-1451.

Dates
Revised: March 2017
First available in Project Euclid: 5 October 2017

https://projecteuclid.org/euclid.aoas/1507168835

Digital Object Identifier
doi:10.1214/17-AOAS1032

Mathematical Reviews number (MathSciNet)
MR3709565

Zentralblatt MATH identifier
1379.62100

#### Citation

Yen, Tso-Jung; Lee, Zong-Rong; Chen, Yi-Hau; Yen, Yu-Min; Hwang, Jing-Shiang. Estimating links of a network from time to event data. Ann. Appl. Stat. 11 (2017), no. 3, 1429--1451. doi:10.1214/17-AOAS1032. https://projecteuclid.org/euclid.aoas/1507168835

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#### Supplemental materials

• Supplementary Materials for “Estimating links of a network from time to event data”. Supplementary Materials contain an numerical algorithm for obtaining estimator (4.4), further details on aggregation of the campaign donation data, additional results for simulation study and additional results for real data application.