Robust Subsampling
52 Pages Posted: 26 Nov 2006 Last revised: 11 Aug 2011
Date Written: July 2011
Abstract
We characterize the robustness of subsampling procedures by deriving a formula for the breakdown point of subsampling quantiles. This breakdown point can be very low for moderate subsampling block sizes, which implies the fragility of subsampling procedures, even if they are applied to robust statistics. This instability arises also for data driven block size selection procedures minimizing the minimum confidence interval volatility index, but can be mitigated if a more robust calibration method can be applied instead. To overcome these robustness problems, we introduce a consistent robust subsampling procedure for M-estimators and derive explicit subsampling quantile breakdown point characterizations for MM-estimators in the linear regression model. Monte Carlo simulations in two settings where the bootstrap fails show the accuracy and robustness of the robust subsampling relative to the subsampling.
Keywords: Subsampling, bootstrap, breakdown point, robustness
JEL Classification: C12, C13, C15
Suggested Citation: Suggested Citation
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