## Electronic Journal of Statistics

### Estimation of the infection parameter of an epidemic modeled by a branching process

Sophie Pénisson

#### Abstract

The aim of this paper is to build estimators of the infection parameter in the different phases of an epidemic (growth and decay phases). The epidemic is modeled by a Markovian process of order $d\geqslant1$, and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, and consequently for different phases of the epidemic. We prove their consistency and asymptotic normality when the number of ancestors (resp. number of generations) tends to infinity.

#### Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2158-2187.

Dates
First available in Project Euclid: 29 October 2014

https://projecteuclid.org/euclid.ejs/1414588190

Digital Object Identifier
doi:10.1214/14-EJS948

Mathematical Reviews number (MathSciNet)
MR3273622

Zentralblatt MATH identifier
1302.62228

#### Citation

Pénisson, Sophie. Estimation of the infection parameter of an epidemic modeled by a branching process. Electron. J. Statist. 8 (2014), no. 2, 2158--2187. doi:10.1214/14-EJS948. https://projecteuclid.org/euclid.ejs/1414588190

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