A locally adaptive penalty for estimation of functionswith varying roughness

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

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume19
Issue number3
DOIs
StatePublished - Sep 2010
Externally publishedYes

Fingerprint

Roughness
Spline
Penalty
Smoothing Splines
Curvature
Kernel Smoother
Function Estimation
Overfitting
Regularization Method
Nonparametric Estimation
Data-driven
Higher Dimensions
Rate of Convergence
Splines
Simulation Study
Methodology
Smoothing splines

Keywords

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

ASJC Scopus subject areas

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

Cite this

A locally adaptive penalty for estimation of functionswith varying roughness. / Storlie, Curtis; Bondell, Howard D.; Reich, Brian J.

In: Journal of Computational and Graphical Statistics, Vol. 19, No. 3, 09.2010, p. 569-589.

Research output: Contribution to journalArticle

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