A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

It is well known that the estimation of the parameters of branching processes (BP) as an important issue used for studying and predicting their behavior needs lots of energy consuming work and faces many computational difficulties. The task is even more complicated in the presence of outliers − "wrong", "untypical" or "contaminated" data, which require a different statistical approach. The existing asymptotic results for the classical estimators can be combined with a generic method for constructing robust estimators, based on the trimmed likelihood and called weighted least trimmed estimators (WLTE). Despite the computational intensity of the procedure it gives well interpretable results even in the case of minor a priori satisfied asymptotic requirements. In the paper we explain the main outlines of this routine and show some classical estimators and their robust modifications in the important class of discrete-time branching processes with immigration. We present a software package for MATLAB for simulation, plotting and estimation of the process parameters. The package is available on the Internet, under the GNU License.