On Estimation of the Variances for Critical Branching Processes with Immigration
نویسنده
چکیده
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 < 3 , the normalizing factor of the estimator for the offspring variance is smaller than √ n, which is different from that of Winnicki (1991).
منابع مشابه
On asymptotic normality of sequential estimators for branching processes with immigration
Consider a Galton–Watson process with immigration. This paper studies the limits of the sequential estimator, proposed by [Sriram, T.N., Basawa, I.V., and Huggins, R.M., (1991). Sequential estimation for branching processes with immigration. Ann. Statist. 19, 2232–2243.] and the modified sequential estimator, proposed by [Shete, S., Sriram, T.N., 1998. Fixed precision estimator of the offspring...
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