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Robust Subsampling

  • Lorenzo Camponovo

    (University of Lugano)

  • Olivier Scaillet

    (University of Geneva and Swiss Finance Institute)

  • Fabio Trojani

    (University of St. Gallen)

We compute the breakdown point of the subsampling quantile of a general statistic, and show that it is increasing in the subsampling block size and the breakdown point of the statistic. These results imply fragile subsampling quantiles for moderate block sizes, also when subsampling procedures are applied to robust statistics. This instability is inherited by data driven block size selection procedures based on the minimum confidence interval volatility (MCIV) index. To overcome these problems, we propose for the linear regression setting a robust subsampling method, which implies a su±ciently high breakdown point and is consistent under standard conditions. Monte Carlo simulations and sensitivity analysis in the linear regression setting show that the robust subsampling with block size selection based on the MCIV index outperforms the subsampling, the classical bootstrap and the robust bootstrap, in terms of accuracy and robustness. These results show that robustness is a key aspect in selecting data driven subsampling block sizes.

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Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 06-33.

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Length: 21 pages
Date of creation: Nov 2006
Date of revision:
Handle: RePEc:chf:rpseri:rp0633
Contact details of provider: Web page: http://www.SwissFinanceInstitute.ch

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  1. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "Applications of subsampling, hybrid, and size-correction methods," Journal of Econometrics, Elsevier, vol. 158(2), pages 285-305, October.
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  8. Salibian-Barrera, Matias & Van Aelst, Stefan & Willems, Gert, 2006. "Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1198-1211, September.
  9. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
  10. Linton, Oliver & Maasoumi, Esfandiar & Whang, Yoon-Jae, 2003. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," SFB 373 Discussion Papers 2003,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  11. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2001.
  12. Salibian-Barrera, Matias, 2006. "Bootstrapping MM-estimators for linear regression with fixed designs," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1287-1297, July.
  13. Loriano Mancini & Elvezio Ronchetti & Fabio Trojani, 2004. "Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2004.04, Institut d'Economie et Econométrie, Université de Genève.
  14. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, 09.
  15. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
  16. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
  17. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators," Journal of Econometrics, Elsevier, vol. 152(1), pages 19-27, September.
  18. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
  19. Romano, Joseph P & Wolf, Michael, 2001. "Subsampling Intervals in Autoregressive Models with Linear Time Trend," Econometrica, Econometric Society, vol. 69(5), pages 1283-1314, September.
  20. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  21. La Vecchia, Davide & Trojani, Fabio, 2010. "Infinitesimal Robustness for Diffusions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 703-712.
  22. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, 05.
  23. Datta, Somnath, 1995. "On a modified bootstrap for certain asymptotically nonnormal statistics," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 91-98, August.
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  25. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  26. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
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