Whittaker and P-spline smoothers; L-curve; V-curve; Cross-Validation
Abstract :
[en] The L-curve is a tool for the selection of the regularization parameter in ill-posed inverse
problems. It is a parametric plot of the size of the residuals vs that of the penalty. The
corner of the L indicates the right amount of regularization. In the context of smoothing
the L-curve is easy to compute and works surprisingly well, even for data with correlated
noise. We present the theoretical background and applications to real data together with an
alternative criterion for finding the corner automatically. We introduce as simplification, the
V-curve, which replaces finding the corner of the L-curve by locating a minimum.
Disciplines :
Mathematics
Author, co-author :
Frasso, Gianluca ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Eilers, Paul H. C.; Erasmus Universiteit Rotterdam - EUR > Department of Biostatistics > Erasmus Medical Centre
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Carmack PS,Spence JS,Schucany WR.Generalised correlated cross-validation.Journal of Nonparametric Statistics. 2012;24:269-82
Currie ID,Durban M.Flexible smoothing with P-splines: a unified approach.Statistical Modelling. 2002;4:333-49
Hipel K,McLeod ATime series modelling of water resources and environmental systems. Amsterdam: Elsevier; 1994:
Hodrick RJ,Prescott EC.Postwar U.S. business cycles: An empirical investigation.Journal of Money, Credit and Banking. 1997;29 (1): 1-16
Hutchinson MF,de Hoog FR.Smoothing noisy data with spline functions.Numerische Mathematik. 1986;50 (3): 311-19
Kauermann G,Krivobokova T,Semmler W.Filtering time series with penalized splines.Studies in Nonlinear Dynamics & Econometrics. 2011;15 (2): 2
Krivobokova T,Kauermann G.A note on penalized spline smoothing with correlated errors.Journal of the American Statistical Association. 2007;102:1328-37
Pandit SM,Wu SMTime series and system analysis with applications. Malabar, Fla: Krieger; 1993:
Ruppert D,Wand P,Carroll RSemiparametric regression. Cambridge: Cambridge University Press; 2003:
Stock J,Watson MIntroduction to econometrics. Boston, MA: Addison–Wesley; 2003:
Vogel CR.Non-convergence of the L-curve regularization parameter selection method.Inverse Problems. 1996;12 (4): 535
Wahba GSpline models for observational data, volume 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: Society for Industrial and Applied Mathematics (SIAM); 1990:
Whittaker ET.On a new method of graduation.Proceedings of the Edinburgh Mathematical Society. 1923;41:63-75
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
