Source: J. Appl. Probab.
Volume 47, Number 2
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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