157
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Robust estimation for boundary correction in wavelet regression

&
Pages 1531-1544 | Received 26 Nov 2010, Accepted 29 Apr 2011, Published online: 05 Jul 2011

References

  • Eubank , R. L. 1988 . Spline Smoothing and Nonparametric Regression , New York : Marcel Dekker .
  • Wahba , G. 1990 . Spline Models for Observational Data , Philadelphia , PA : SIAM .
  • Takezawa , K. 2006 . Introduction to Nonparametric Regression , Hoboken , NJ : John Wiley .
  • Donoho , D. L. and Johnstone , I. M. 1994 . Ideal spatial adaptation by wavelet shrinkage . Biometrika , 81 : 425 – 455 .
  • Donoho , D. L. and Johnstone , I. M. 1995 . Adapting to unknown smoothness via wavelet shrinkage . J. Amer. Statist. Assoc , 90 ( 432 ) : 1200 – 1224 .
  • Oh , H. S. , Naveau , P. and Lee , G. 2001 . Polynomial boundary treatment for wavelet regression . Biometrika , 88 : 291 – 298 .
  • Johnstone , I. M. and Silverman , B. W. 2005 . Empirical Bayes selection of wavelet thresholds . Ann. Statist , 33 : 1700 – 1752 .
  • Maronna , R. , Martin , R. and Yohai , V. 2006 . Robust Statistics , New York : Wiley .
  • Oh , H. S. and Lee , T. C.M. 2005 . Hybrid local polynomial wavelet shrinkage: Wavelet regression with automatic boundary adjustment . Comput. Statist. Data Anal , 48 ( 4 ) : 809 – 820 .
  • Oh , H. S. , Nychka , D. W. and Lee , T. C.M. 2007 . The role of pseudo data for robust smoothing with application to wavelet regression . Biometrika , 94 : 893 – 904 .
  • Oh , H. S , Kim , D. and Kim , Y. 2009 . Robust wavelet shrinkage using robust selection of thresholds . Statist. Comput , 19 ( 1 ) : 27 – 34 .
  • Oh , H. S. , Lee , J. and Kim , D. 2008 . A recipe for robust estimation using pseudo data . J. Korean Statist. Soc , 37 ( 1 ) : 63 – 72 .
  • Nason , G. P. 1996 . Wavelet shrinkage by cross-validation . Roy. Statist. Soc. B , 58 : 463 – 479 .
  • Abramovich , F. , Bailey , T. C. and Sapatinas , T. 2000 . Wavelet analysis and its statistical applications . The Statistician , 49 : 1 – 29 .
  • Lee , T. and Oh , H. S. 2004 . Automatic polynomial wavelet regression . Statist. Comput , 14 : 337 – 341 .
  • Mallows , C. L. 1973 . Some comments on Cp . Technometrics , 15 : 661 – 675 .
  • Schwarz , G. 1978 . Estimating the dimension of a model . Ann. Statist , 6 ( 2 ) : 461 – 464 .
  • Johnstone , I. M. and Silverman , B. W. Empirical Bayes selection of wavelet thresholds . unpublished manuscript (2003)
  • Oh , H.-S. and Kim , H.-M. 2008 . Bayesian automatic polynomial wavelet regression . J. Statist. Plann. Inference , 138 ( 8 ) : 2303 – 2312 .
  • Hastie , T. and Tibshirani , R. 1990 . Generalized Additive Models , London : Chapman & Hall .
  • Yohai , V. J. 1987 . High breakdown-point and high efficiency robust estimates for regression . Ann. Statist , 15 : 642 – 656 .
  • Salibian-Barrera , M. and Yohai , V. J. 2006 . A fast algorithm for S-regression estimates . J. Comput. Graph. Statist , 15 ( 2 ) : 414 – 427 .
  • Croux , C. , Dehaene , G. and Hoorelbeke , D. “ Robust standard errors for robust estimators ” . Discussion Papers Series 03.16, K.U. Leuven, 2003
  • Shao , J. 1996 . Bootstrap model selection . J. Amer. Statist. Assoc , 91 ( 434 ) : 655 – 665 .
  • McQuarrie , A. D.R. and Tsai , C. L. 1998 . Regression and Time Series Model Selection , Singapore : World Scientific .
  • Imon , A. H.M.R. and Ali , M. M. 2005 . Bootstrapping regression residuals . J. Korean Statist. Soc , 16 : 665 – 682 .
  • Uraibi , H. , Midi , H. , Talib , B. and Yousif , J. 2009 . Linear regression model selection based on robust bootstrapping technique . Am. J. Appl. Sci , 6 : 1191 – 1198 .
  • Wand , M. P. 2000 . A comparison of regression spline smoothing procedures . Comput. Statist , 15 : 443 – 462 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.