Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Minimum Hellinger distance estimation for Controlled Branching Processes
Carmen Minuesa Abril

Last modified: 2014-04-01


Controlled branching processes are useful probabilistic models with which to describe population dynamics in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The probabilistic theory of controlled branching processes, in particular the study of its extinction problem and its limiting behaviour, has been extensively investigated. The behaviour of these populations is associated to the main parameters of the offspring  and control distributions, consequently, an important question is to study the inferential problems arising from this model. We focus our attention on supercritical controlled branching processes with a parametric scheme for the offspring distribution. The purpose of this work is to consider the minimum Hellinger distance estimator of the underlying offspring parameter and to study the asymptotical normality of this estimator and its efficiency at the true model and robustness against gross errors. The provided results extend those given in Sriram, T.N. and Vidyashankar, A.N. (Minimum Hellinger distance estimation for supercritical Galton-Watson processes, Statistic and Probability Letters 50, 331-342, 2000).


Acknowledgements: The research was supported by the Ministerio de Economía y Competitividad, Junta de Extremadura and the FEDER through the grants MTM2012-31235 and GR10118.