Limit laws of estimators for critical multi-type Galton-Watson processes

Details Limit laws of estimators for critical multi-type Galton-Watson processes Limit laws of estimators for critical multi-type Galton-Watson processes

2005-03-24

arxiv.org/abs/math/0503552v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1992-2015

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000521 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000521

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.

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