In this paper, the asymptotic behavior of the conditional least squares (CLS) estimators of the offspring means (α, β) and of the criticality parameter := α + β for a 2-type critical doubly symmetric positively regular Galton-Watson branching process with immigration is described.

We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.Keywords Continuous state and continuous time branching processes with immigration · Branching and immigration mechanisms · Conditional least squares estimator · Non-normal asymptotic limit behaviour Mathematics Subject Classification 62F12 · 60J80

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.

We study asymptotic behavior of conditional least squares estimators for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.

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