A locally adaptive penalty for estimation of functionswith varying roughness

Curtis B. Storlie, Howard D. Bondell, Brian J. Reich

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We propose a new regularization method called Loco-Spline for nonparametric function estimation. Loco-Spline uses a penalty which is data driven and locally adaptive. This allows for more flexible estimation of the function in regions of the domain where it has more curvature, without over fitting in regions that have little curvature. This methodology is also transferred into higher dimensions via the Smoothing Spline ANOVA framework. General conditions for optimal MSE rate of convergence are given and the Loco-Spline is shown to achieve this rate. In our simulation study, the Loco-Spline substantially outperforms the traditional smoothing spline and the locally adaptive kernel smoother. Code to fit Loco-Spline models is included with the Supplemental Materials for this article which are available online.

Original languageEnglish (US)
Pages (from-to)569-589
Number of pages21
JournalJournal of Computational and Graphical Statistics
Issue number3
StatePublished - Sep 2010


  • L-Spline
  • Local bandwidth
  • Nonparametric regression
  • Regularization method
  • Spatially adaptive smoothing

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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