J Austral Math Soc Ser A 58 pp47--53, 1995.

The Limiting Distribution of a Recursive Resampling Procedure

Zheng Zukang and Wu Lipeng

Abstract

A recursive resampling method is discussed in this paper. Let X₁, X₂, ..., X_n be i.i.d. random variables with distribution function F and construct the empirical distribution function F_n. A new sample X_{n + 1} is drawn from F_n and the new empirical distribution function ~F_{n + 1} in the wide sense, is computed from X₁, X₂, ..., X_n, X_{n + 1}. Then X_{n + 2} is drawn from ~F_{n + 1} and ~F_{n + 2} is obtained. In this way, X_{n + m} and ~F_{n + m} are found. It will be proved that ~F_{n + 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 redirection in unconditional variance.

1991 AMS Subject Classification: 60G50, 60F15

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Authors

Zheng Zukang

Wu Lipeng

Department of Statistics and Operations Research, Fudan University, Shanghai, 200433, China.