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September, 1993 Spline Smoothing with an Estimated Order Parameter
Michael L. Stein
Ann. Statist. 21(3): 1522-1544 (September, 1993). DOI: 10.1214/aos/1176349270


Smoothing splines of a fixed order are commonly used as nonparametric regression estimates. The only parameter, then, that needs to be estimated is the smoothing parameter, which is often estimated using some form of cross validation. This work allows the order of the smoothing spline to be estimated using a model in which the order parameter is continuous. Within this setting, generalized cross validation and modified maximum likelihood estimates of the order and smoothing parameters are compared. I show that there are both stochastic and fixed regression functions for which modified maximum likelihood yields asymptotically better estimates of the regression function than generalized cross validation. These results are supported by a small simulation study, although there are functions for which the asymptotic results can be misleading even for fairly large sample sizes.


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Michael L. Stein. "Spline Smoothing with an Estimated Order Parameter." Ann. Statist. 21 (3) 1522 - 1544, September, 1993.


Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0786.62052
MathSciNet: MR1241277
Digital Object Identifier: 10.1214/aos/1176349270

Primary: 62G07
Secondary: 62M20

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 3 • September, 1993
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