Seminars 2007— Abstracts

Friday February 16

Speaker: Chris Field, Dalhousie University, Halifax

Title: Bootstrapping Clustered Data

Abstract: A number of different bootstraps have been proposed for bootstrapping clustered data from one-way arrays. The simulation results in the literature suggest that some of these methods work quite well in practice; the theoretical results are limited and more mixed in their conclusions. For example, McCullagh (2000) reaches negative conclusions about the use of nonparametric bootstraps for one-way arrays. In this talk, I'd like to extend our understanding of the issues by discussing the impact of different ways of modelling clustered data, 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 from (ii) nonparametric bootstraps to include model-based bootstraps. We determine that the consistency of variance estimates for a bootstrap method depends on the choice of model with the residual bootstrap giving consistency under the transformation model while the cluster bootstrap gives consistent estimates under both the transformation and random effect model. In addition we note that the criteria based on the distribution of the bootstrap observations are not really useful in assessing consistency.

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