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

Zhiyi Chi
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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.

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Zhiyi Chi. 2005-03-24. Limit laws of estimators for critical multi-type Galton-Watson processes. https://doi.org/10.1214/105051604000000521

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