The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 4 (2004), 1992-2015.
Limit laws of estimators for critical multi-type Galton–Watson processes
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.
Ann. Appl. Probab., Volume 14, Number 4 (2004), 1992-2015.
First available in Project Euclid: 5 November 2004
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.aoap/1099674086