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Asymptotic Expansions for Array Branching Processes with Applications to Bootstrapping

Part of: Stochastic processes Distribution theory Markov processes

Published online by Cambridge University Press:  14 July 2016

T. N. Sriram
T. N. Sriram*
Affiliation:
University of Georgia
*
∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
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Abstract

Asymptotic expansions are obtained for the distribution function of a studentized estimator of the offspring mean sequence in an array branching process with immigration. The expansion result is shown to hold in a test function topology. As an application of this result, it is shown that the bootstrapping distribution of the estimator of the offspring mean in a sub-critical branching process with immigration also admits the same expansion (in probability). From these considerations, it is concluded that the bootstrapping distribution provides a better approximation asymptotically than the normal distribution.

Keywords

Edgeworth expansionsmartingalestest function topologybootstrappingarray branching processes

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 62E20: Asymptotic distribution theory
Secondary: 60G09: Exchangeability 60G42: Martingales with discrete parameter

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 12 - 26
Copyright
Copyright © Applied Probability Trust 1998 

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