The Annals of Applied Probability

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

Zhiyi Chi

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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.

Article information

Ann. Appl. Probab., Volume 14, Number 4 (2004), 1992-2015.

First available in Project Euclid: 5 November 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F05: Central limit and other weak theorems

Branching processes stable distribution noncentral limit theorem mean matrix Frobenius eigenvector eigenvalue


Chi, Zhiyi. Limit laws of estimators for critical multi-type Galton–Watson processes. Ann. Appl. Probab. 14 (2004), no. 4, 1992--2015. doi:10.1214/105051604000000521.

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