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Principle of Duality in Cubic Smoothing Spline

Author

Listed:
  • Ruixue Du

    (Graduate School of Social Sciences, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan)

  • Hiroshi Yamada

    (School of Informatics and Data Science, Hiroshima University, 1-2-1 Kagamiyama, Higashi-Hiroshima 739-8525, Japan)

Abstract

Fitting a cubic smoothing spline is a typical smoothing method. This paper reveals a principle of duality in the penalized least squares regressions relating to the method. We also provide a number of results derived from them, some of which are illustrated by a real data example.

Suggested Citation

  • Ruixue Du & Hiroshi Yamada, 2020. "Principle of Duality in Cubic Smoothing Spline," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1839-:d:431152
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    References listed on IDEAS

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    2. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    3. Hiroshi Yamada, 2018. "Several least-squares problems related to the Hodrick–Prescott filtering," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1022-1027, March.
    4. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    5. Yamada, Hiroshi, 2020. "A Smoothing Method That Looks Like The Hodrick–Prescott Filter," Econometric Theory, Cambridge University Press, vol. 36(5), pages 961-981, October.
    6. Hiroshi Yamada, 2020. "A note on Whittaker–Henderson graduation: Bisymmetry of the smoother matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(7), pages 1629-1634, April.
    7. Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
    8. Hiroshi Yamada, 2018. "Why does the trend extracted by the Hodrick–Prescott filtering seem to be more plausible than the linear trend?," Applied Economics Letters, Taylor & Francis Journals, vol. 25(2), pages 102-105, January.
    9. Hiroshi Yamada, 2017. "The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10897-10902, November.
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