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Journal of Probability and Statistics
Volume 2014, Article ID 203469, 11 pages
Research Article

Direct Determination of Smoothing Parameter for Penalized Spline Regression

Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-8580, Japan

Received 7 January 2014; Revised 31 March 2014; Accepted 31 March 2014; Published 22 April 2014

Academic Editor: Dejian Lai

Copyright © 2014 Takuma Yoshida. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Penalized spline estimator is one of the useful smoothing methods. To construct the estimator, having goodness of fit and smoothness, the smoothing parameter should be appropriately selected. The purpose of this paper is to select the smoothing parameter using the asymptotic property of the penalized splines. The new smoothing parameter selection method is established in the context of minimization asymptotic form of MISE of the penalized splines. The mathematical and the numerical properties of the proposed method are studied. First we organize the new method in univariate regression model. Next we extend to the additive models. A simulation study to confirm the efficiency of the proposed method is addressed.