Fast robust estimation of prediction error based on resampling

Computational Statistics and Data Analysis

Volumn 54, Issue 12, 2010, Pages 3121-3130

  Khan, Jafar A ^a   Van Aelst, Stefan ^b   Zamar, Ruben H ^c  

^a UNIVERSITY OF DHAKA   (Bangladesh)

^b GHENT UNIVERSITY   (Belgium)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bootstrap; Cross validation; Prediction error; Robustness

Indexed keywords

FORECASTING; ROBUSTNESS (CONTROL SYSTEMS);

BOOTSTRAP; CROSS VALIDATION; FAST APPROXIMATION; PREDICTION ERRORS; REGRESSION PARAMETERS; RESAMPLING TECHNIQUE; ROBUST ESTIMATION; ROBUST REGRESSIONS;

ERRORS;

EID: 77955346396     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.01.031     Document Type: Article

References (32)

1. Efron, B., 1983. Estimating the error rate of a prediction rule: Improvement on cross-validation. J. Amer. Statist. Assoc. 78, 316-331.
2. Gatu, C., Kontoghiorghes, E.J., 2006. Branch-and-bound algorithms for computing the best subset regression models. J. Comput. Graph. Statist. 15, 139-156.
3. Hastie, T., Tibshirani, R., Friedman, J., 2009. The Elements of Statistical Learning, 2nd ed. Springer.
4. Hawkins, D.M., Bradu, D., Kass, G.V., 1984. Location of several outliers in multiple regression data using elemental sets. Technometrics 26, 197-208. (Pubitemid 14627777)
5. Hofmann, M., Gatu, C., Kontoghiorghes, E.J., 2007. Efficient algorithms for computing the best subset regression models for large-scale problems. Comput. Statist. Data Anal. 52, 16-29.
6. Hubert, M., Engelen, S., 2007. Fast cross-validation of high-breakdown resampling algorithms for PCA. Comput. Statist. Data Anal. 51, 5013-5024.
7. Hubert, M., Rousseeuw, PJ., Van Aelst, S., 2008. High-breakdown robust multivariate methods. Statist. Sci. 23, 92-119.
8. Khan, J.A., 2006. Robust linear model selection for high-dimensional datasets. Unpublished Doctoral Thesis, University of British Columbia, Dept. of Statistics.
9. Khan, J.A., Van Aelst, S., Zamar, R.H., 2007a. Building a robust linear model with forward selection and stepwise procedures. Comput. Statist. Data Anal. 52, 239-248.
10. Khan, J.A., Van Aelst, S., Zamar, R.H., 2007b. Robust linear model selection based on least angle regression. J. Amer. Statist. Assoc. 102, 1289-1299.
11. Kim, J.-H., 2009. Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap. Comput. Statist. Data Anal. 53, 3735-3745.
12. Loisel, S., Takane, M., 2009. Fast indirect robust generalized method of moments. Comput. Statist. Data Anal. 53, 3571-3579.
13. Lutz, R.W., Kalisch, M., Bühlmann, P., 2008. Robustified L2 boosting. Comput. Statist. Data Anal. 52, 3331-3341.
14. Maronna, R.A., Martin, R.D., Yohai, V.J., 2006. Robust Statistics: Theory and Methods. John Wiley and Sons.
15. McCann, L., Welsch, R.E., 2007. Robust variable selection using least angle regression and elemental set sampling. Comput. Statist. Data Anal. 52, 249-257.
16. Miller, A., 2002. Subset Selection in Regression. Chapman & Hall/CRC.
17. Morgenthaler, S., Welsch, R.E., Zenide, A., 2003. Algorithms for robust model selection in linear regression. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (Eds.), Theory and Applications of Recent Robust Methods. Birkhäuser-Verlag, Basel, Switzerland, pp. 195-206.
18. R Development Core Team, 2009. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN: 3-900051-07-0. URL: http://www.R-project.org/.
19. Robustbase Development Team, 2008. Robustbase: Basic robust statistics. R package version 0.4-3. URL: http://cran.R-project.org/package-robustbase.
20. Roelant, E., Van Aelst, S., Croux, C., 2009. Multivariate generalized S-estimators. J. Multivariate Anal. 100, 876-887.
21. Rousseeuw, P.J., Van Aelst, S., Van Driessen, I.C., Agulló, J., 2004. Robust multivariate regression. Technometrics 46, 293-305.
22. Rousseeuw, P.J., Yohai, V.J., 1984. Robust regression by means of S-estimators. In: Franke, J., Hardle, W., Martin, D. (Eds.), Robust and NonlinearTime Series. In: Lecture Notes in Statist., vol. 26. Springer-Verlag, Berlin, pp. 256-272.
23. Salibian-Barrera, M., Van Aelst, S., 2008. Robust model selection using fast and robust bootstrap. Comput. Statist. Data Anal. 52, 5121-5135.
24. Salibian-Barrera, M., Van Aelst, S., Willems, G. 2006. PCA based on multivariate MM-estimators with fast and robust bootstrap. J. Amer. Statist. Assoc. 101, 1198-1211.
25. Salibian-Barrera, M., Willems, G., Zamar, R.H., 2008. The fast-tau estimator for regression. J. Comput. Graph. Statist. 17, 659-682.
26. Salibian-Barrera, M., Yohai, V.J., 2006. A fast algorithm for S-regression estimates. J. Comput. Graph. Statist. 15, 414-427.
27. Salibian-Barrera, M., Zamar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582.
28. Serneels, S., Filzmoser, P., Croux, C., Van Espen, P.J., 2005. Robust continuum regression. Chemometr. Intell. Lab. Syst. 76, 197-204.
29. Shao, J., 1993. Linear model selection by cross-validation. J. Amer. Statist. Assoc. 88, 486-494.
30. Van Aelst, S., Willems, G., 2005. Multivariate regression S-estimators for robust estimation and inference. Statist. Sinica 15, 981-1001. (Pubitemid 43098289)
31. Willems, G., Van Aelst, S., 2005. Fast and robust bootstrap for LTS. Comput. Statist. Data Anal. 48, 703-715.
32. Yohai, V.J., 1987. High breakdown point and high efficiency robust estimates for regression. Ann. Statist. 15, 642-656.