On estimation of the variances for critical branching processes with immigration release_sjfl2bljhbftfe4mdtvojmejke

Abstract

The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 &amp;lt; α &amp;lt; 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √<jats:italic>n</jats:italic>, which is different from that of Winnicki (1991).
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