Nonparametric estimation for Galton--Watson type process

B. L. S. Prakasa Rao

Statistics & Probability Letters, 1992, vol. 13, issue 4, 287-293

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.

Keywords: Nonparametric; estimator; Galton--Watson; type; process; consistency (search for similar items in EconPapers)
Date: 1992
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