Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Asymptotic Optimality of CL and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing

Ker-Chau Li
The Annals of Statistics
Vol. 14, No. 3 (Sep., 1986), pp. 1101-1112
Stable URL: http://www.jstor.org/stable/3035560
Page Count: 12
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Optimality of CL  and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing
Preview not available

Abstract

The asymptotic optimality of Mallows' CL and generalized cross-validation is demonstrated in the setting of ridge regression. An application is made to spline smoothing in nonparametric regression. A counterexample is given to help understand why sometimes GCV may not be asymptotically optimal. The coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of GCV. The proff is based on the connection between GCV and Stein's unbiased risk estimate.

Page Thumbnails

  • Thumbnail: Page 
1101
    1101
  • Thumbnail: Page 
1102
    1102
  • Thumbnail: Page 
1103
    1103
  • Thumbnail: Page 
1104
    1104
  • Thumbnail: Page 
1105
    1105
  • Thumbnail: Page 
1106
    1106
  • Thumbnail: Page 
1107
    1107
  • Thumbnail: Page 
1108
    1108
  • Thumbnail: Page 
1109
    1109
  • Thumbnail: Page 
1110
    1110
  • Thumbnail: Page 
1111
    1111
  • Thumbnail: Page 
1112
    1112