Fixedbsubsampling and the block bootstrap: improved confidence sets based onp-value calibration

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2013 · Volume 75 · Issue 1

DOI: 10.1111/j.1467-9868.2012.01037.x

Abstract

Summary.Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the bandwidth. We propose to adopt the fixedbapproach, as advocated by Kiefer and Vogelsang in the heteroscedasticity–auto-correlation robust testing context, to account for the influence of the bandwidth on inference. Under the fixedbasymptotic framework, we derive the asymptotic null distribution of thep-values for subsampling and the moving block bootstrap, and further propose a calibration of the traditional small-b-based confidence intervals (regions or bands) and tests. Our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters, such as the marginal distribution function. Simulation results show that the fixedbapproach is more accurate than the traditional smallbapproach in terms of approximating the finite sample distribution, and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts.

Keywords

Block bootstrap, Calibration, Iterative bootstrap, Prepivoting, Subsampling

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