Minimum disparity estimation in controlled branching processes

TL;DR

This paper introduces robust minimum disparity estimators for controlled branching processes, demonstrating their consistency, asymptotic normality, and robustness through theoretical proofs and simulation studies.

Contribution

It develops and analyzes minimum disparity estimators within controlled branching processes, including robustness properties and asymptotic behavior, under general conditions.

Findings

Estimators are consistent and asymptotically normal.

Both Hellinger and negative exponential disparities are robust to outliers.

Negative exponential disparity also robust to inliers.

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, it is discussed the robustness of the estimators proposed. Through a simulated example, focussing on the minimum Hellinger and negative exponential disparity estimators, it is shown that both are robust against outliers, being the negative exponential one also robust against inliers.