REDUCING BIAS WITHOUT PREJUDICING SIGN

PETER HALL^{1}, BRETT PRESNELL^{1} AND BERWIN A. TURLACH^{1,2}

1 Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia 2 Co-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.