Prakasa Rao, B. L. S. (1992) Nonparametric estimation for Galton-Watson type process Statistics & Probability Letters, 13 (4). pp. 287-293. ISSN 0167-7152
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/016771...
Related URL: http://dx.doi.org/10.1016/0167-7152(92)90036-5
Abstract
A stochastic process {Xn, n ≥ 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 ≥ 0, n ≥ 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Nonparametric Estimator; Galton—Watson Type Process; Consistency |
| ID Code: | 37286 |
| Deposited On: | 11 Apr 2011 15:27 |
| Last Modified: | 26 Apr 2011 10:48 |
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