Abstract
For a sub-critical Galton-Watson process $\mathbf{X}$ with immigration, estimators have been studied by Pakes (1971) for the mean of the stationary distribution of $\mathbf{X}$, and by Nanthi (1979) for the offspring mean and the immigration mean of $\mathbf{X}$. These estimators have been shown by them to be asymptotically normal. In this paper it is shown that they have a joint limiting distribution which is singularly normal.
Citation
K. N. Venkataraman. K. Nanthi. "A Limit Theorem on a Subcritical Galton-Watson Process with Immigration." Ann. Probab. 10 (4) 1069 - 1074, November, 1982. https://doi.org/10.1214/aop/1176993730
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