We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton–Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees and frequencies of types within trees, a higher-order asymptotic of the “relative frequency” estimator of the left eigenvector of the mean matrix, a higher-order joint asymptotic of the maximum likelihood estimators of the offspring probabilities and the consistency of an estimator of the right eigenvector of the mean matrix, are established.
Publié le : 2004-11-14
Classification:
Branching processes,
stable distribution,
noncentral limit theorem,
mean matrix,
Frobenius eigenvector,
eigenvalue,
60J80,
60F05
@article{1099674086,
author = {Chi, Zhiyi},
title = {Limit laws of estimators for critical multi-type Galton--Watson processes},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 1992-2015},
language = {en},
url = {http://dml.mathdoc.fr/item/1099674086}
}
Chi, Zhiyi. Limit laws of estimators for critical multi-type Galton–Watson processes. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 1992-2015. http://gdmltest.u-ga.fr/item/1099674086/