Statistical inference of 2-type critical Galton-Watson processes with immigration

TL;DR

This paper investigates the asymptotic properties of estimators for the offspring mean matrix and criticality parameter in 2-type critical Galton-Watson processes with immigration, including subcritical cases.

Contribution

It provides new asymptotic analysis of estimators for the offspring mean matrix and spectral radius in 2-type Galton-Watson processes with immigration.

Findings

Asymptotic behavior of conditional least squares estimators characterized

Analysis includes subcritical case considerations

Results applicable to critical positively regular processes

Abstract

In this paper the asymptotic behavior of the conditional least squares estimators of the offspring mean matrix for a 2-type critical positively regular Galton-Watson branching process with immigration is described.We also study this question for a natural estimator of the spectral radius of the offspring mean matrix, which we call criticality parameter. We discuss the subcritical case as well.