The Annals of Applied Probability

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

Zhiyi Chi

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 5 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1099674086

Digital Object Identifier
doi:10.1214/105051604000000521

Mathematical Reviews number (MathSciNet)
MR2099660

Zentralblatt MATH identifier
1060.62028

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

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

Citation

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


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