Robust Subsampling

We characterize the robustness of subsampling procedures by deriving a general 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 is applied instead. To overcome these robustness problems, we propose a robust subsampling method for linear models, which is consistent under standard conditions. Monte Carlo simulations and sensitivity analysis show that the robust subsampling with calibrated block size selection outperforms the classical subsampling, the classical bootstrap and the robust bootstrap, in terms of accuracy and robustness.