Journal article

Robust subsampling

  • Camponovo, Lorenzo Università della Svizzera italiana, Svizzera
  • Scaillet, Olivier University of Geneva and Swiss Finance Institute
  • Trojani, Fabio Istituto di finanza (IFin), Facoltà di scienze economiche, Università della Svizzera italiana, Svizzera
Published in:
  • Journal of econometrics. - Elsevier. - 2012, vol. 167, no. 1, p. 197-210
English 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 when 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 robustsubsampling 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 robustsubsampling relative to the subsampling.
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