UBC Statistics Department




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Statistics 526 Term 2 1998-99
Smoothing Methods in Regression

Course Information

INSTRUCTOR: Nancy Heckman

nancy@stat.ubc.ca

822-3595

TENTATIVE OUTLINE

Overview of smoothing:

- playing around in Splus, overfitting versus oversmoothing, "by eye" choice of smoothing parameter, effective number of parameters

Standard least squares (normal likelihood) methods:

- Kernel and local polynomial methods: definition, asymptotic bias and variance, optimal bandwidth, data driven choice of bandwidth (plug in versus cross-validation)

- Regression methods: B-splines

- Penalized methods: smoothing splines

Using other likelihoods with the above standard methods (this can cover quite a range - like all of parametric statistics!)

After this, topics will depend on people's interest. Possible topics:

- correlated data

- additive models

- shapes of curves

- wavelets (I know nothing about these but am willing to learn)

- .....

WORK FOR COURSE

There will be no exams.

Course work will be homework, projects, and presentations/discussions.

PREREQUISITES

IDEAL BACKGROUND:

- some mathematical statistics (one semester of Bickel and Doksum)

- some experience with regression analysis

- Splus experience

HOWEVER:

Prerequisites are very flexible. I've taught the course with students who have not had the ideal background, and we've managed. I do lots of Splus examples. Projects/homework/presentations can be geared towards your skill set, while still pushing you to expand your skill set!

TEXT/REFERENCES

There is no text for the course. I have some latexed class notes (currently under revision). We'll also use articles and parts of different books.

Here are some books on smoothing, with my comments. They are on 1 day reserve at UBC.

Eubank, R. (1988). Spline Smoothing and Nonparametric Regressions.

Fan, Jianqing and Gijbels (1996). Local polynomial modelling and its applications. Hmmmm. This one is missing and I've requested that it be replaced.

Green, P.J. and B.W. Silverman (1994). Nonparametric Regression and Generalized Linear Models. This book covers penalized likelihood methods.

Hardle, W. (1990). Applied Nonparametric Regression.

Hastie, T. and R. Tibshirani (1990). Generalized Additive Models. Chapters 1 - 3 give a nice summary of smoothing methods and ideas.

Simonoff, J. (1996). Smoothing methods in statistics. Nice overview, not very theoretical, pretty practical.

Wand, M. and C. Jones (1995). Kernel Smoothing. Mainly local polynomical methods.