On estimation of the variances for critical branching processes with immigration
Chunhua Ma and Longmin Wang
Source: J. Appl. Probab. Volume 47, Number 2
(2010), 526-542.
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 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).
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Keywords: Branching process with immigration; regular variation; conditional least squares estimator; limiting distribution
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784907
Digital Object Identifier: doi:10.1239/jap/1276784907
Zentralblatt MATH identifier: 05758485
Mathematical Reviews number (MathSciNet): MR2668504
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