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B0574
Title: Minimum disparity estimators for the offspring parameters of controlled branching processes Authors:  Miguel Gonzalez Velasco - University of Extremadura (Spain) [presenting]
Carmen Minuesa Abril - University of Extremadura (Spain)
Ines M del Puerto - University of Extremadura (Spain)
Abstract: In the context of discrete-time stochastic processes, one of the most interesting generalizations of the Bienayme-Galton-Watson process is the controlled branching process (CBP). This model is characterized by the fact that the number of individuals with reproductive capacity in each generation is controlled by a random control function. Furthermore, an important issue in the inference theory of branching processes is the development of robust estimation methodologies. In connection with this question, we consider the minimum disparity estimators of the underlying offspring parameters of a CBP. We assume that the offspring distribution belongs to a general parametric family. First, we obtain these estimators considering that the entire family tree up to a certain generation can be observed. After that we consider two incomplete data schemes: that given by the total number of individuals and progenitors in each generation, and the one given only by the population sizes. We examine the asymptotic and robustness properties of the estimators proposed. Measures for robustness qualities against gross errors are also studied. The results are illustrated by simulated examples developed by the statistical software R.