Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 1, 107--122

A Note On Estimation In Multitype Supercritical Branching Processes With Immigration


SANJAY SHETE, University of Texas M.D. Anderson

Cancer Center, Houston, USA and T.N. SRIRAM, University of Georgia, Athens, USA

SUMMARY. For multitype branching processes with immigration, weighted conditional least squares estimator of the mean matrix $M$ and the maximal eigenvalue $\rho$ of $M$ are developed based on little more information about the process than just the generation sizes.  For the supercritical case, strong consistency and asymptotic normality of the estimators are established.  Comparisons in terms of asymptotic variances show that the weighted conditional least squares estimators derived here are as good as the maximum likelihood estimators obtained by Asmussen and Keiding (1978) under the full family tree information.

AMS (1991) subject classification. Primary 60J80; secondary 62M05.

Key words and phrases. Supercritical, weighted conditional least squares, maximal eigenvalue, martingales, invariance principle.

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