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The limiting distribution of a recursive resampling procedure

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

Zheng Zukang  and
Wu Lipeng
Zheng Zukang
Affiliation:
Department of Statistics and Operations Research, Fudan University, Shanghai, 200433, China
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Abstract

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A recursive resampling method is discussed in this paper. Let X1, X2,…, Xn, be i.i.d. random variables with distribution function F and construct the empirical distribution function Fn. A new sample Xn+1 is drawn from Fn and the new empirical distribution function 1 in the wide sense, is computed from X1, X2,…, Xn, Xn+1. Then Xn+2 is drawn from 1 and 2 is obtained. In this way, Xn+m and m are found. It will be proved that m converges to a random variable almost surely as m goes to infinity and the limiting distribution is a compound beta distribution. In comparison with the usual non-recursive bootstrap, the main advantage of this procedure is a reduction in unconditional variance.

MSC classification

Secondary: 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 1 , February 1995 , pp. 47 - 53
Copyright
Copyright © Australian Mathematical Society 1995

References

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