310
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Locally optimal adaptive smoothing splines

&
Pages 665-680 | Received 12 Oct 2011, Accepted 09 May 2012, Published online: 26 Jun 2012

References

  • Abramovich , F. and Grinshtein , V. 1999 . Derivation of Equivalent Kernel for General Spline Smoothing: A Systematic Approach . Bernoulli , 5 : 359 – 379 .
  • Abramovich , F. and Steinberg , D. M. 1996 . Improved Inference in Nonparametric Regression Using Lk-Smoothing Splines . Journal of Statistical Planning and Inference , 49 : 327 – 341 .
  • Craven , P. and Wahba , G. 1979 . Smoothing Noisy Data with Spline Functions . Numerische Mathematik , 31 : 377 – 403 .
  • Cummins , D. J. , Filloon , T. G. and Nychka , D. 2001 . Confidence Intervals for Nonparametric Curve Estimates: Toward More Uniform Pointwise Coverage . Journal of the American Statistical Association , 96 : 233 – 246 .
  • Donoho , D. L. and Johnstone , I. M. 1995 . Adapting to Unknown Smoothness via Wavelet Shrinkage . Journal of the American Statistical Association , 90 : 1200 – 1224 .
  • Friedman , J. H. 1991 . Multivariate Adaptive Regression Splines . The Annals of Statistics , 19 : 1 – 67 .
  • Herrmann , E. 1997 . Local Bandwidth Choice in Kernel Regression Estimation . Journal of Graphical and Computational Statistics , 6 : 35 – 54 .
  • Liu , Z. and Guo , W. 2010 . Data Driven Adaptive Spline Smoothing . Statistica Sinica , 20 : 1143 – 1163 .
  • Luo , Z. and Wahba , G. 1997 . Hybrid Adaptive Splines . Journal of the American Statistical Association , 92 : 10 – 116 .
  • Mallows , C. L. 1973 . Some Comments on Cp . Technometrics , 15 : 661 – 675 .
  • Muller , H. G. and Stadmuller , U. 1987 . Variable Bandwidth Kernel Estimators of Regression Curves . The Annals of Statistics , 15 : 182 – 201 .
  • Nychka , D. 1988 . Bayesian Confidence Intervals for Smoothing Splines . Journal of the American Statistical Association , 83 : 1134 – 1143 .
  • Pintore , A. , Speckman , P. and Holmes , C. C. 2006 . Spatially Adaptive Smoothing Splines . Biometrika , 93 : 113 – 125 .
  • Ramsay , J. O. and Silverman , B. W. 1996 . Functional Data Analysis , New York : Springer .
  • Rice , J. and Rosenblatt , M. 1983 . Smoothing Splines: Regresion, Derivatives and Deconvolution . The Annals of Statistics , 11 : 141 – 156 .
  • Ruppert , D. and Carroll , R. J. 2000 . Spatially-Adaptive Penalties for Spline Fitting . Australian and New Zealand Journal of Statistics , 42 : 205 – 223 .
  • Silverman , B. W. 1984 . Spline Smoothing: The Equivalent Variable Kernel Method . The Annals of Statistics , 12 : 898 – 916 .
  • Silverman , B. W. 1985 . Some Aspects of the Spline Smoothing Approaches to Non-Parametric Regressoin Curve Fitting . Journal of the Royal Statistical Society, Series B , 47 : 1 – 52 .
  • Sklar , J. C. , Wu , J. , Meiring , W. and Wang , Y. 2012 . Non-Parametric Regression with Basis Selection from Multiple Libraries . Technometrics , to appear.
  • Stone , M. 1974 . Cross-Validation and Multinomial Prediction . Biometrika , 61 : 509 – 515 .
  • Stone , C. J. 1982 . Optimal Global Rates of Convergence for Nonparametric Regression . The Annals of Statistics , 10 : 1040 – 1053 .
  • Storlie , C. B. , Bondell , H. D. and Reich , B. J. 2010 . A Locally Adaptive Penalty for Estimation of Functions with Varying Roughness . Journal of Computational and Graphical Statistics , 19 : 569 – 589 .
  • Wahba , G. 1975 . Smoothing Noisy Data with Spline Functions . Numerische Mathematik , 24 : 383 – 393 .
  • Wahba , G. 1983 . Bayesian “Confidence Intervals” for the Cross-Validated Smoothing Spline . Journal of the Royal Statistical Society, Series B , 45 : 133 – 150 .
  • Wahba , G. 1990 . Spline Models for Observational Data , Philadelphia : SIAM: CCBMS-NSF Regional Conference Series in Applied Mathematics .

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.