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Nonparametric estimation for Galton--Watson type process

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  • Prakasa Rao, B. L. S.

Abstract

A stochastic process {Xn, n [greater-or-equal, slanted] 0} with X0 = 1 is said to be a Galton--Watson type process if {Xn} is a non-negative valued Markov process such that E[e-tXn + 1 Xn] = e-h(t)Xn, t [greater-or-equal, slanted] 0, n [greater-or-equal, slanted] o where h(·) is the cumulant generating function of the random variable X1 with an infinitely divisible off-spring distribution. Here we study a nonparametric kernel-type estimator of h(·) based on the observations X1,...,Xn. Consistency property of this estimator is investigated.

Suggested Citation

  • Prakasa Rao, B. L. S., 1992. "Nonparametric estimation for Galton--Watson type process," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 287-293, March.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:4:p:287-293
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