Minimum disparity estimation in controlled branching processes

Abstract

Minimum disparity estimation in controlled branching processes is dealt with by assuming that the offspring law belongs to a general parametric family. Under some regularity conditions it is proved that the minimum disparity estimators proposed -based on the nonparametric maximum likelihood estimator of the offspring law when the entire family tree is observed- are consistent and asymptotic normally distributed. Moreover, the robustness of the estimators proposed is discussed. Through a simulated example, focusing on the minimum Hellinger and negative exponential disparity estimators, it is shown that both are robust against outliers, and the minimum negative exponential estimator is also robust against inliers.