Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Pseudosplines

Trevor Hastie
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 58, No. 2 (1996), pp. 379-396
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345983
Page Count: 18
  • Read Online (Free)
  • Download ($29.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Pseudosplines
Preview not available

Abstract

We describe a method for constructing a family of low rank, penalized scatterplot smoothers. These pseudosplines have shrinking behaviour that is similar to that of smoothing splines. They require two ingredients: a basis and a penalty sequence. The smoother is then computed by a generalized ridge regression. The family can be used to approximate existing high rank smoothers in terms of their dominant eigenvectors. Our motivating example uses linear combinations of orthogonal polynomials to approximate smoothing splines, where the linear combination and the penalty sequence depend on the particular instance of the smoother being approximated. As a leading application, we demonstrate the use of these pseudosplines in additive model computations. Additive models are typically fitted by an iterative smoothing algorithm, and any features other than the fit itself are difficult to compute. These include standard error curves, degrees of freedom, generalized cross-validation and influence diagnostics. By using a low rank pseudospline approximation for each of the smoothers involved, the entire additive fit can be approximated by a corresponding low rank approximation. This can be computed exactly and efficiently, and opens the door to a variety of computations that were not feasible before.

Page Thumbnails

  • Thumbnail: Page 
[379]
    [379]
  • Thumbnail: Page 
380
    380
  • Thumbnail: Page 
381
    381
  • Thumbnail: Page 
382
    382
  • Thumbnail: Page 
383
    383
  • Thumbnail: Page 
384
    384
  • Thumbnail: Page 
385
    385
  • Thumbnail: Page 
386
    386
  • Thumbnail: Page 
387
    387
  • Thumbnail: Page 
388
    388
  • Thumbnail: Page 
389
    389
  • Thumbnail: Page 
390
    390
  • Thumbnail: Page 
391
    391
  • Thumbnail: Page 
392
    392
  • Thumbnail: Page 
393
    393
  • Thumbnail: Page 
394
    394
  • Thumbnail: Page 
395
    395
  • Thumbnail: Page 
396
    396