Limit laws of estimators for critical multi-type Galton-Watson processes (Q1769421)

A multi-type Galton-Watson is called critical if the largest eigenvalue of its mean matrix is \(1\). For such a process, a branching tree is finite with probability \(1\), but the expectation of its size is infinite. The author considers the asymptotics of some estimators based on a large sample of terminating branching trees, and the asymptotics refer to the probabilistic behavior as the sample size \(n\to\infty\). For related papers see: \textit{J. P. Dion} and \textit{N. M. Yanev} [J. Statist. Plann. Inference 39, 329--351 (1994; Zbl 0808.62074), J. Appl. Probab. 34, 309--327 (1997; Zbl 0895.60091)]; \textit{S. M. Stigler} [Biometrika 58, 499--508 (1971; Zbl 0226.62039)]; and \textit{N. M. Yanev} [Theory Probab. Appl. 20, 612--622 (1975; Zbl 0363.60073)].