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Splines, knots, and penalties
Author(s) -
Eilers Paul H. C.,
Marx Brian D.
Publication year - 2010
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.125
Subject(s) - mathematics , smoothing , spline (mechanical) , nonparametric regression , smoothing spline , extrapolation , econometrics , regression , algorithm , statistics , computer science , spline interpolation , structural engineering , engineering , bilinear interpolation
Penalized splines have gained much popularity as a flexible tool for smoothing and semi‐parametric models. Two approaches have been advocated: (1) use a B‐spline basis, equally spaced knots, and difference penalties [Eilers PHC, Marx BD. Flexible smoothing using B‐splines and penalized likelihood (with Comments and Rejoinder). Stat Sci 1996, 11:89–121.] and (2) use truncated power functions, knots based on quantiles of the independent variable and a ridge penalty [Ruppert D, Wand MP, Carroll RJ. Semiparametric Regression. New York: Cambridge University Press; 2003]. We compare the two approaches on many aspects: numerical stability, quality of the fit, interpolation/extrapolation, derivative estimation, visual presentation and extension to multidimensional smoothing. We discuss mixed model and Bayesian parallels to penalized regression. We conclude that B‐splines with difference penalties are clearly to be preferred. WIREs Comp Stat 2010 2 637–653 DOI: 10.1002/wics.125 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Density Estimation