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On the asymptotic behaviour of the jackknife for stochastic processes

Published online by Cambridge University Press:  17 April 2009

P.N. Kokic  and
N.C. Weber
P.N. Kokic
Affiliation:
Department of Mathematical Statistics, University of Sydney, Sydney, New South Wales 2006, Australia.
N.C. Weber
Affiliation:
Department of Mathematical Statistics, University of Sydney, Sydney, New South Wales 2006, Australia.
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Abstract

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The limiting behaviour of the J∞ jackknife estimator for parameters associated with stochastic processes is shown to depend on the nature of the underlying process through the asymptotic behaviour of the estimator being jackknifed. In particular, the jackknifed versions of certain estimators associated with renewal processes are shown to have an asymptotic normal distribution.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 329 - 337
Copyright
Copyright © Australian Mathematical Society 1983

References

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[3]Gray, H.L., Watkins, T.A. and Adams, J.E., “On the jackknife statistic, its extensions, and its relation to en-transformations”, Ann. Math. Statist. 43 (1972), 1–30.CrossRefGoogle Scholar
[4]Watkins, T.A., “Jackknifing stochastic processes” (PhD dissertation, Texas Technical University, Texas, 1971).Google Scholar