Robust Cross Validation Score

Park, Dong-Ryeon

  • 발행 : 2005.08.01


Consider the problem of estimating the underlying regression function from a set of noisy data which is contaminated by a long tailed error distribution. There exist several robust smoothing techniques and these are turned out to be very useful to reduce the influence of outlying observations. However, no matter what kind of robust smoother we use, we should choose the smoothing parameter and relatively less attention has been made for the robust bandwidth selection method. In this paper, we adopt the idea of robust location parameter estimation technique and propose the robust cross validation score functions.


Cross validation;Local regression;Location parameter estimators;Robust regression


  1. Bowman, A. (1984), An alternative method of cross-validation for the smoothing of density estimates, Biometrika, 71, 353-360
  2. Cantoni, E. and Ronchetti, E. (2001), Resistant selection of the smoothing parameter for smoothing splines, Statistics and Computing, 11, 141-146
  3. Cleveland, W. (1979), Robust locally weighted regression and smoothing scatterplots, Journal of the American Statistical Association, 74, 829-836
  4. Fan, J. (1993), Local linear regression smoothers and their minimax efficiency, The Annals of Statistics, 21, 196-216
  5. Fan, J. and Gijbels, I. (1995), Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. Journal of Royal Statistical Society, Series B, 57, 371-394
  6. Fan, J. and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, Chapman & Hall, London
  7. Gasser, T. and Muller, H. (1979), Kernel estimation of regression functions. In Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics, 757, 23-68, Springer-Verlag, New York
  8. Hoaglin, D., Mosteller, F. and Tukey, J. (1983), Understanding Robust and Exploratory Data Analysis, John Wiley & Sons, New York
  9. Jones, M., Marron, J. and Sheather, S. (1996), A brief survey of bandwidth selection for density estimation, Journal of the American Statistical Association, 91, 401-407
  10. Loader, C. (1999a), Bandwidth selection: classical or plug-in?, The Annals of Statistics, 27, 415-438
  11. Loader, C. (1999b), Local Regression and Likelihood, Spring-Verlag, New York
  12. Park, D. (2004), Robustness weight by weighted median distance, Computational Statistics, 19, 367-383
  13. Rice, J. (1984), Bandwidth choice for nonparametric regression, The Annals of Statistics, 12, 1215-1230
  14. Rousseeuw, P. and Leroy, A. (1987), Robust Regression and Outlier Detection, John Wiley & Sons, New York
  15. Ruppert, D. and Wand, M. (1994), Multivariate locally weighted least squares regression, The Annals of Statistics, 22, 1346-1370
  16. Wand, M. and Jones, M. (1995), Kernel Smoothing, Chapman & Hall, London
  17. Wang, F. and Scott, D. (1994), The $L_1$ method for robust nonparametric regression, Journal of the American Statistical Association, 89, 249-260
  18. Fan, J. (1992),. Design-adaptive nonparametric regression, Journal of the American Statistical Association, 87, 998-1004
  19. Fan, J. and Gijbels, I. (1992), Variable bandwidth and local linear regression smoothers, The Annals of Statistics, 20, 2008-2036