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Ohio State University logo STAT 763 Reading & Notes

This web page contains a tentative course schedule (subject to change), a list of topics to be covered in class, relevant references, and some useful links. Also, class handouts, if any, will be posted here as we go along. The three books are abbreviated as CG (Chong Gu), GW (Grace Wahba), and GS (Green and Silverman) for reference below.

Topics and References

  1. Week 1

    Introduction to smoothing splines (CG 1.1, GW Foreword, GS Ch1),
    Splines for interpolation and smoothing (GS 2.1-2.3),
    Natural splines, B-splines (de Boor : A Practical Guide to Splines).
    Read this interview with Carl de Boor.

    For historical notes on smoothing splines, see CG 1.6 (Sec1.1) and GW Foreword.

    [March 29 - 31] Introduction to Smoothing Splines | R code for smoothing, interpolating splines and B-splines.

  2. Week 2

    General perspective on penalized least squares methods (CG 2.2-2.3),
    Two illustrative examples:
    1) A finite dimensional example (penalized one-way ANOVA) (CG 2.2).

    [April 5 - April 7] Two examaples
    Stein's Paradox in Statistics, Bradley Efron and Carl Morris, Scientific American, 236, pp. 119-127 (1977).

  3. Week 3

    2) Smoothing splines (CG 2.3, GW 1.2-1.3).
    Functional analytic approach to smoothing splines (CG 2.3, GW 1.2-1.3),
    Characterizing the solution to the smoothing problem.

    Here is the website for Grace Wahba's Golden Oldies,
    where Kimeldorf and Wahba (1971) can be found.

  4. Week 4

    Smoothing splines in statistical perspective:
    Influence of the tuning parameter on smoother matrix (CG 3.1, GW 1.3)

    [April 21 - 28] Smoothing splines in statistical perspective

  5. Week 5

    Smoothing parameter selection, cross-validation (CG 3.2, GW 4.2-4.3)

  6. Week 6

    Smoothing splines as Bayes estimates (CG 2.5, GW 1.5, GS 3.8),
    Confidence intervals (CG 3.3, GW Ch 5).

  7. Week 7

    Numerical examples (CG 3.5).

    [May 5] Numerical examples
    R code for simulation and analysis of Canadian income data (from R library SemiPar)
    R documentation of smooth.spline and R library gss

    Introduction to Reproducing Kernel Hilbert Spaces (CG 2.1, GW 1.1).

    [May 12-17] Reproducing Kernel Hilbert Spaces
    - Introduction to Hilbert Space (P. Halmos), Chapter 1. The Geometry of Hilbert Space for background.

  8. Week 8

    Properties of reproducing kernels (CG 2.1, 2.4).
    N. Aronszajn (1950), Theory of Reproducing kernels

    [May 19] Grace Wahba visits our class!

  9. Week 9

    Smoothing Spline ANOVA models (CG 3.1, GW Ch 10).

    [May 24-26] SS ANOVA
    R code for plotting some basis functions of W_2[0,1]*W_2[0,1]

  10. Week 10

    [May 31] Memorial Day (no class)

    Numerical example of SS ANOVA models (CG 3.5).

    [June 2] R code for SS-ANOVA example
    R implementation of SS-ANOVA modeling: gss package


[Acknowledgements] The instructor thanks Grace Wahba and Chong Gu for their generosity of providing class notes.

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