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Spatially adaptive smoothing splines

Author

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  • Alexandre Pintore
  • Paul Speckman
  • Chris C. Holmes

Abstract

We use a reproducing kernel Hilbert space representation to derive the smoothing spline solution when the smoothness penalty is a function λ(t) of the design space t, thereby allowing the model to adapt to various degrees of smoothness in the structure of the data. We propose a convenient form for the smoothness penalty function and discuss computational algorithms for automatic curve fitting using a generalised crossvalidation measure. Copyright 2006, Oxford University Press.

Suggested Citation

  • Alexandre Pintore & Paul Speckman & Chris C. Holmes, 2006. "Spatially adaptive smoothing splines," Biometrika, Biometrika Trust, vol. 93(1), pages 113-125, March.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:1:p:113-125
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    File URL: http://hdl.handle.net/10.1093/biomet/93.1.113
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    Citations

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    Cited by:

    1. Jang, Dongik & Oh, Hee-Seok, 2011. "Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1029-1040, February.
    2. P.L. Davies & M. Meise, 2008. "Approximating data with weighted smoothing splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 207-228.
    3. Dongik Jang & Hee-Seok Oh & Philippe Naveau, 2017. "Identifying local smoothness for spatially inhomogeneous functions," Computational Statistics, Springer, vol. 32(3), pages 1115-1138, September.
    4. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    5. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    6. Fabio Centofanti & Antonio Lepore & Alessandra Menafoglio & Biagio Palumbo & Simone Vantini, 2023. "Adaptive smoothing spline estimator for the function-on-function linear regression model," Computational Statistics, Springer, vol. 38(1), pages 191-216, March.
    7. Kim, Daeju & Kawano, Shuichi & Ninomiya, Yoshiyuki, 2023. "Smoothly varying regularization," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    8. Nielsen, J.D. & Dean, C.B., 2008. "Adaptive functional mixed NHPP models for the analysis of recurrent event panel data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3670-3685, March.
    9. Rakêt, Lars Lau & Markussen, Bo, 2014. "Approximate inference for spatial functional data on massively parallel processors," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 227-240.
    10. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.

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