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Martingale central limit theorems and asymptotic estimation theory for multitype branching processes
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- Journal:
- Advances in Applied Probability / Volume 10 / Issue 1 / March 1978
- Published online by Cambridge University Press:
- 01 July 2016, pp. 109-129
- Print publication:
- March 1978
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- Article
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This paper considers the problem of estimating the growth rate ρ of a p-type Galton–Watson process {Zn}. To this end, a general approach of possible independent interest to central limit theorems for discrete-time branching processes is developed. The idea is to adapt martingale central limit theory to martingale difference triangular arrays indexed by the set of all individuals ever alive. Iterated logarithm laws are derived by similar methods. Asymptotic distribution results and the a.s. asymptotic behaviour are derived for a maximum likelihood estimator based upon all parent–offspring combinations in a given number N of generations, and for the estimator
which depends on the total generation sizes 
only.
which depends on the total generation sizes 
only.