IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Robust subsampling

  • Camponovo, Lorenzo
  • Scaillet, Olivier
  • Trojani, Fabio

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 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0304407611002594
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 1 ()
Pages: 197-210

as
in new window

Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:197-210
DOI: 10.1016/j.jeconom.2011.11.005
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Han Hong & Olivier Scaillet & Elie Tamer, 2001. "A Fast Subsampling Method for Nonlinear Dynamic Models," Working Papers 2001-39, Centre de Recherche en Economie et Statistique.
  2. Datta, Somnath, 1995. "On a modified bootstrap for certain asymptotically nonnormal statistics," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 91-98, August.
  3. Loriano Mancini & Elvezio Ronchetti & Fabio Trojani, 2005. "Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models," University of St. Gallen Department of Economics working paper series 2005 2005-01, Department of Economics, University of St. Gallen.
  4. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, 05.
  5. 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.
  6. Davide La Vecchia & Fabio Trojani, 2008. "Infinitesimal Robustness for Diffusions," University of St. Gallen Department of Economics working paper series 2008 2008-09, Department of Economics, University of St. Gallen.
  7. Salibian-Barrera, Matias, 2006. "Bootstrapping MM-estimators for linear regression with fixed designs," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1287-1297, July.
  8. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
  9. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
  10. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
  11. 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.
  12. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Applications of Subsampling, Hybrid, and Size-Correction Methods," Cowles Foundation Discussion Papers 1608, Cowles Foundation for Research in Economics, Yale University.
  13. Russell Davidson & Emmanuel Flachaire, 2006. "Asymptotic And Bootstrap Inference For Inequality And Poverty Measures," Departmental Working Papers 2005-06, McGill University, Department of Economics.
  14. 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.
  15. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, 09.
  16. Kim, Tae-Hwan & White, Halbert & Stone, Douglas, 2000. "Asymptotic and Bayesian Confidence Intervals for Sharpe Style Weights," University of California at San Diego, Economics Working Paper Series qt5h98h28m, Department of Economics, UC San Diego.
  17. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
  18. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
  19. 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.
  20. Donald W.K. Andrews, 1999. "Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators," Cowles Foundation Discussion Papers 1230, Cowles Foundation for Research in Economics, Yale University.
  21. 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.
  22. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
  23. 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.
  24. 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.
  25. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
  26. Lee, Stephen M.S. & Pun, M.C., 2006. "On m out of n Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1185-1197, September.
  27. Matias Salibian-Barrera, 2006. "The Asymptotics of MM-Estimators for Linear Regression with Fixed Designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(3), pages 283-294, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:167:y:2012:i:1:p:197-210. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.