Robust Subsampling

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

See all articles by Lorenzo Camponovo

Lorenzo Camponovo

University of St. Gallen

O. Scaillet

University of Geneva GSEM and GFRI; Swiss Finance Institute; University of Geneva - Research Center for Statistics

Fabio Trojani

Swiss Finance Institute; University of Geneva

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

University of St. Gallen ( email )

Varnbuelstr. 14
Saint Gallen, St. Gallen CH-9000
Switzerland

Olivier Scaillet

University of Geneva GSEM and GFRI ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland
+ 41 22 379 88 16 (Phone)
+41 22 389 81 04 (Fax)

HOME PAGE: http://www.scaillet.ch

Swiss Finance Institute

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

University of Geneva - Research Center for Statistics

Geneva
Switzerland

Fabio Trojani (Contact Author)

Swiss Finance Institute ( email )

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

University of Geneva ( email )

Geneva, Geneva
Switzerland

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