A non-iterative optimization method for smoothness in penalized spline regression

Typically, an optimal smoothing parameter in a penalized spline regression is determined by minimizing an information criterion, such as one of the C p , CV and GCV criteria. Since an explicit solution to the minimization problem for an information criterion cannot be obtained, it is necessary to ca...

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Bibliographic Details
Published in:Statistics and computing 2012-03, Vol.22 (2), p.527-544
Main Author: Yanagihara, Hirokazu
Format: Article
Language:English
Subjects:
Artificial Intelligence
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:Typically, an optimal smoothing parameter in a penalized spline regression is determined by minimizing an information criterion, such as one of the C p , CV and GCV criteria. Since an explicit solution to the minimization problem for an information criterion cannot be obtained, it is necessary to carry out an iterative procedure to search for the optimal smoothing parameter. In order to avoid such extra calculation, a non-iterative optimization method for smoothness in penalized spline regression is proposed using the formulation of generalized ridge regression. By conducting numerical simulations, we verify that our method has better performance than other methods which optimize the number of basis functions and the single smoothing parameter by means of the CV or GCV criteria.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-011-9245-0