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Biometrika 1995 82(3):561-574;
© 1995 by Biometrika Trust
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On blocking rules for the bootstrap with dependent data

PETER HALL1, JOEL L. HOROWITZ2 and BING-YI JING3

1 Centre for Mathematics and its Applications, Australian National University Canberra, ACT 0200, Australia
2 Department of Economics, University of Iowa Iowa City, Iowa 52242-1000, USA
3 Department of Mathematics, Hong Kong University of Science and Technology Hong Kong

Received for publication 1 May 1993. Revision received 1 January 1995.
  Abstract

We address the issue of optimal block choice in applications of the block bootstrap to dependent data. It is shown that optimal block size depends significantly on context, being equal to n1/3, n1/4 and n1/5 in the cases of variance or bias estimation, estimation of a onesided distribution function, and estimation of a two-sided distribution function, respectively. A clear intuitive explanation of this phenomenon is given, together with outlines of theoretical arguments in specific cases. It is shown that these orders of magnitude of block sizes can be used to produce a simple, practical rule for selecting block size empirically. That technique is explored numerically.

Key Words: Autoregression • Bias • Blocking methods • Bootstrap • Mean squared error • Variance


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