Limit laws of estimators for critical multi-type Galton-Watson processes
Abstract
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.
Cite
@article{arxiv.math/0503552,
title = {Limit laws of estimators for critical multi-type Galton-Watson processes},
author = {Zhiyi Chi},
journal= {arXiv preprint arXiv:math/0503552},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/105051604000000521 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)