Let $\{X_n\}$ be the branching process with immigration and let $m$ and $\lambda$ be the means of the offspring and immigration distributions, respectively. Estimation results for $m$ and $\lambda$ were obtained in the literature for the subcritical $(m < 1)$ and supercritical $(m > 1)$ cases, but no unified estimation procedure was developed, which would allow inference without knowledge of the range of $m$. The goal of this paper is to investigate this problem.
Publié le : 1990-12-14
Classification:
Branching process with immigration,
conditional least squares,
weighted conditional least squares,
inconsistency,
limiting distribution,
62M99,
62M05
@article{1176347876,
author = {Wei, C. Z. and Winnicki, J.},
title = {Estimation of the Means in the Branching Process with Immigration},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1757-1773},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347876}
}
Wei, C. Z.; Winnicki, J. Estimation of the Means in the Branching Process with Immigration. Ann. Statist., Tome 18 (1990) no. 1, pp. 1757-1773. http://gdmltest.u-ga.fr/item/1176347876/