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An Estimated General Cross Validation Function for Periodic Control Theoretic Smoothing Splines

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Perspectives in Mathematical System Theory, Control, and Signal Processing

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 398))

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Abstract

In this paper, a method is developed for estimating the optimal smoothing parameter ε for periodic control theoretic smoothing splines. The procedure is based on general cross validation (GCV) and requires no a priori information about the underlying curve or level of noise in the measurements. The optimal ε is the minimizer of an estimated GCV cost function, which is derived based on a discretization of the L 2 smoothing problem for periodic control theoretic smoothing splines.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Maja Karasalo & Xiaoming Hu

  2. Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, USA

    Clyde F. Martin

Authors
  1. Maja Karasalo
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  2. Xiaoming Hu
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  3. Clyde F. Martin
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Editor information

Editors and Affiliations

  1. ESAT, K.U.Leuven, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Jan C. Willems

  2. Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656, Tokyo, Japan

    Shinji Hara

  3. Control Systems Theory Group, Department of Applied Mathematics and Physics , Graduate School of Informatics, Kyoto University, Yoshida-honmachi, 606-8501, Kyoto, Japan

    Yoshito Ohta

  4. Dept. Applied Analysis & Complex Dynamic Systems, Kyoto University, 606-8501, Kyoto, Japan

    Hisaya Fujioka

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Karasalo, M., Hu, X., Martin, C.F. (2010). An Estimated General Cross Validation Function for Periodic Control Theoretic Smoothing Splines. In: Willems, J.C., Hara, S., Ohta, Y., Fujioka, H. (eds) Perspectives in Mathematical System Theory, Control, and Signal Processing. Lecture Notes in Control and Information Sciences, vol 398. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93918-4_9

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  • DOI: https://doi.org/10.1007/978-3-540-93918-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93917-7

  • Online ISBN: 978-3-540-93918-4

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