It has been found, under a smooth function model setting, that the conventional bootstrap is inconsistent at stationary points of the smooth function and that the m out of n bootstrap succeeds in restoring consistency, provided that a correct convergence rate can be specified of the plug-in smooth function estimator. We re-investigate the properties of the bootstrap in a moving-parameter framework, and show that neither the conventional bootstrap nor the m out of n bootstrap are uniformly consistent over the parameter space. The results reflect to some extent finite-sample anomalies that cannot be explained by conventional, fixed-parameter, asymptotics. We propose a weighted bootstrap procedure for constructing uniformly consistent bootstrap confidence intervals, which does not require explicit specification of the convergence rate of the smooth function estimator. Our findings are illustrated with several numerical examples to compare the coverage accuracies of the different bootstrap procedures.

The 11th International Conference on Robust Statistics (ICORS 2011), Valladolid, Spain, 27 June-1 July 2011. In Abstracts Book of the 11th ICORS, 2011, p. 83, abstract 109

Session CS6 - Contributed Session

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