Robust Subsampling

52 Pages Posted: 26 Nov 2006 Last revised: 11 Aug 2011

See all articles by Lorenzo Camponovo

Lorenzo Camponovo

(SUPSI) Scuola universitaria professionale della Svizzera italiana

O. Scaillet

Swiss Finance Institute - University of Geneva

Fabio Trojani

University of Geneva; University of Turin - Department of Statistics and Applied Mathematics; Swiss Finance Institute

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

Camponovo, Lorenzo and Scaillet, Olivier and Trojani, Fabio, Robust Subsampling (July 2011). Swiss Finance Institute Research Paper No. 06-33, Available at SSRN: https://ssrn.com/abstract=947112 or http://dx.doi.org/10.2139/ssrn.947112

Lorenzo Camponovo

(SUPSI) Scuola universitaria professionale della Svizzera italiana ( email )

Le Gerre
Manno, CA Canton Ticino CH-6928
Switzerland

Olivier Scaillet

Swiss Finance Institute - University of Geneva ( email )

Geneva
Switzerland

Fabio Trojani (Contact Author)

University of Geneva ( email )

Geneva, Geneva
Switzerland

University of Turin - Department of Statistics and Applied Mathematics ( email )

Piazza Arbarello, 8
Turin, I-10122
Italy

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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