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What can or can't be estimated in branching and related processes?

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  • Maki, Ellen
  • McDunnough, Philip

Abstract

Estimation of the underlying distribution is considered for the incompletely observed random walk and the incompletely observed Galton--Watson branching tree. Based on infrequent observation of a random walk, parameters not completely determined by the first few moments of the underlying distribution cannot be consistently estimated. A similar result is given for the branching tree when observations are sums of family sizes. When the offspring distribution belongs to the power series family MLE's are obtained from an approximate likelihood.

Suggested Citation

  • Maki, Ellen & McDunnough, Philip, 1989. "What can or can't be estimated in branching and related processes?," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 307-314, April.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:2:p:307-314
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    Cited by:

    1. Manuel Mendoza & Eduardo Gutiérrez-Peña, 2000. "Bayesian conjugate analysis of the Galton-Watson process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 149-171, June.

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