JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY 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 n"/3, n"/4 and nll5 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.
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