Sampling a branching tree

Ellen Maki and Philip McDunnough

Stochastic Processes and their Applications, 1989, vol. 31, issue 2, 283-305

Abstract: A Galton-Watson branching tree is sampled, yielding a derived vector process of family sizes. Exact and asymptotic distributions for this process are derived, rates of convergence given, and the probability of selecting different families is shown to converge rapidly to one. Consistent, asymptotically normal nonparametric estimates of the underlying offspring distribution are obtained and for power series distributions approximate MLE's are shown to be asymptotically normal and efficient.

Keywords: branching; process; sampling; inference; in; stochastic; processes; likelihood; inference; asymptotic; theory (search for similar items in EconPapers)
Date: 1989
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