AISM 52, 507-518

Reducing bias without prejudicing sign

Peter Hall1, Brett Presnell1 and Berwin A. Turlach1,2

1Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia
2Co-operative Research Centre in Advanced Computational Systems, Australian National University, Canberra, ACT 0200, Australia

(Received February 12, 1998; revised February 8, 1999)

Abstract.    Jackknife and bootstrap bias corrections are based on a differencing argument which does not necessarily respect the sign of the true parameter value. Depending on sampling variability they can over-correct, producing a final estimator that is negative when one knows on physical grounds that it should be positive. To overcome this problem we suggest a simple, alternative bootstrap approach, based on biased-bootstrap methods. Our technique has similar properties to the standard uniform-bootstrap method in cases where the latter does not endanger sign, but it respects sign in a canonical way when the standard method disregards it.

Key words and phrases:    Bias reduction, biased bootstrap, bootstrap, jackknife, twicing, weighted bootstrap.

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