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Biometrika 1976 63(2):315-321; doi:10.1093/biomet/63.2.315
© 1976 by Biometrika Trust
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Sharpening the jackknife

T. SHAROT

Audits of Great Britain, Eastcote, Middlesex

The jackknife is now well known as a widely applicable bias-reduction tool, with the added advantages of Tukey's variance estimator, and in certain applications, a gain in precision. In this paper a new family of jackknives is introduced, together with a variance estimator. The family includes the ordinary, first-order, and second-order jackknives as special cases and the variance estimator includes Tukey's as a special case. A sample-based decision rule for choosing a member of the family, intended to achieve a gain in precision over either order of jackknife, is given. The success of the rule is examined by simulation in estimation of the reciprocal of the parent mean and in ratio estimation.

Key Words: Bias reduction • Jackknife • Simulation • Variance estimator • Variance reduction


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