๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Efficient algorithms for robust generalized cross-validation spline smoothing

โœ Scribed by Mark A. Lukas; Frank R. de Hoog; Robert S. Anderssen

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
278 KB
Volume
235
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

โœฆ Synopsis

Generalized cross-validation (GCV) is a widely used parameter selection criterion for spline smoothing, but it can give poor results if the sample size n is not sufficiently large. An effective way to overcome this is to use the more stable criterion called robust GCV (RGCV). The main computational effort for the evaluation of the GCV score is the trace of the smoothing matrix, tr A, while the RGCV score requires both tr A and tr A 2 . Since 1985, there has been an efficient O(n) algorithm to compute tr A. This paper develops two pairs of new O(n) algorithms to compute tr A and tr A 2 , which allow the RGCV score to be calculated efficiently. The algorithms involve the differentiation of certain matrix functionals using banded Cholesky decomposition.

๐Ÿ“œ SIMILAR VOLUMES

Surface approximation by spline smoothin
Surface approximation by spline smoothing and generalized cross-validation
โœ Hongmin Lu; Frank H. Mathis ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 505 KB

Lu, H. and F.H. Mathis, Surface approximation by spline smoothing and generalized cross-validation, Mathematics and Computers in Simulation 34 (1992) 541-549. A technique is developed to approximate multi-dimensional surfaces based on smoothing splines. The tensor product is used to extend a one-di

An efficient algorithm for generating B-
An efficient algorithm for generating B-spline interpolation curves and surfaces from B-spline approximations
โœ Wang, Hui Ping ;Hewgill, Denton E. ;Vickers, Geoffrey W. ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Wiley (John Wiley & Sons) ๐ŸŒ English โš– 302 KB ๐Ÿ‘ 1 views

A useful and simple algorithm is presented for interactively generating B-spline interpolation curves and surfaces from B-spline approximation solutions. The difference between the data points and the B-spline approximation is used to modify the control vertices in order to generate a succession of

Generalized cross-validation as a stoppi
Generalized cross-validation as a stopping rule for the Richardson-Lucy algorithm
โœ Stanley J. Reeves ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 488 KB

The Richardson-Lucy (R-L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation-maximization (EM) algorithm applied to Poisson data. The R-L method is iterative in nature and converges to a (possibly local) maximum of the likeliho