Bootstrapping Clustered Data

Abstract

A number of different bootstraps have been proposed for bootstrapping clustered data from one-way arrays. The simulation results of Andersson and Karlsson (2001) suggest that some of these methods work quite well in practice; the theoretical results are limited and more mixed in their conclusions. In particular, McCullagh (2000) reaches negative conclusions about the use of (nonparametric) bootstraps for one-way arrays. The purpose of this paper is to extend our understanding of the issues by discussing the criteria for successful bootstraps used in the literature and extending the theory from (i) functions of the sample mean to include functions of the between and within sums of squares and (ii) nonparametric bootstraps to include model-based bootstraps. We obtain some unexpected conclusions about the existing criteria and reach a positive view of the prospects for bootstrapping clustered data. Joint Work with C.A. Field, Department of Mathematics and Statistics Dalhousie University, Halifax N.S., Canada