Statistical Methods & Applications

, Volume 21, Issue 2, pp 169–191 | Cite as

Asymptotic distribution of martingale estimators for a class of epidemic models

  • Raúl FierroEmail author


This article is a contribution to the asymptotic inference on the parameters of a quite general class of stochastic models for the spread of epidemics developing in closed populations. Various epidemic models are contained within our framework, for instance, a stochastic version of the Kermack and McKendrick model and the SIS epidemic model. Each model belonging to this class, which consists in a family of discrete-time stochastic process, contains certain parameters to be estimated by means of martingale estimators. Some particular cases defined by means of Markov chains are included in our setting. The main aim of this work is to prove consistency and asymptotic normality of these estimators. Some hypothesis tests based on the main results are also shown.


Stochastic epidemic models Hypothesis testing Asymptotic normality Basic reproduction number 


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© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Instituto de MatemáticaPontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Centro de Investigación y Modelamiento de Fenómenos AleatoriosUniversidad de ValparaísoValparaísoChile

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