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A New Method for the Model Selection in B-Spline Surface Approximation with an Influence Function
Science Journal of Applied Mathematics and Statistics
Volume 1, Issue 5, December 2013, Pages: 38-46
Received: Aug. 27, 2013; Published: Oct. 20, 2013
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Hongmei Bao, Graduate School of Environmental Science, Okayama University, Okayama, Japan
Kaoru Fueda, Graduate School of Environmental and Life Science, Okayama University, Okayama, Japan
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In model selection, the most effective method requires much time.The analysis of the bivariate B-spline model with a penalized term has many difficulties.It has many factors and parameters such the number of the knots, the locations of those knots, number of B-spline functions and the value of the smoothing parameter of the penalized term.For the determination of the model we have to compare a large amount of the combinations of those parameters. Various information criteria are considered and the cross validation (CV) criterion is excellent but it requires a large amount of computational costs. The effect of the influence function and the techniques of the generalized cross validation (CV) are considered. The influence function is related to the first term of a Taylor expansion. Some alternative methods are tested and a new method is proposed. For the verification of this method theoretical proof and the computational results are shown.
B-Spline Surface, Generalized Information Criterion, Influence Function, Generalized Cross-Validation, Cross-Validation, Kullback-Leibler Divergence, Surface Model Selection
To cite this article
Hongmei Bao, Kaoru Fueda, A New Method for the Model Selection in B-Spline Surface Approximation with an Influence Function, Science Journal of Applied Mathematics and Statistics. Vol. 1, No. 5, 2013, pp. 38-46. doi: 10.11648/j.sjams.20130105.11
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