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Biometrika 1990 77(1):179-185;
© 1990 by Biometrika Trust
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Bootstrap bias

G. A. YOUNG and H. E. DANIELS

Statistical Laboratory, University of Cambridge Cambridge CB2 JSB, U.K.

Received for publication 1 February 1989. Revision received 1 July 1989.
  Abstract

Use of the bootstrap in estimation of the sampling distribution of a pivot is considered for two simple situations. It is shown by a simulation study that in each case the bootstrap is noticeably biased for small sample sizes. The techniques of computer algebra are used to obtain an exact assessment of the bias in both problems and an approximate theoretical analysis based on saddlepoint approximation is presented.

Key Words: Bias • Bootstrap • Computer algebra • Pivot • Saddlepoint approximation • Tail probability


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