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Smoothing has become an established part of the statistical toolbox and it is finding its way into most of the statistical software packages. There exists a wide choice of methods, like smoothing splines, regression splines, kernel smoothing and local likelihood. It is difficult for the novice to make an informed choice.
The main theme of our course is the use of a combination of local basis functions (B-splines) and roughness penalties: the P-spline approach. This smoother stays as close as possible to established regression methodology, with many advantages:
compact computations;
compact results (a small set of coefficients);
easily computed diagnostics: cross-validation or AIC, standard errors, effective degrees of freedom;
parametric models are obtained as limiting cases of heavy smoothing;
straightforward extension to non-normal data, along the lines of the generalized linear model;
useful for density estimation, with well-behaved boundaries;
P-splines are ideal building blocks for generalized additive models, varying-coefficient models and signal regression.
We present the basic theory and illustrate it with many practical examples: scatterplot smoothing, trend lines, density estimation, dose-response curves, smooth high dimensional coefficient vectors, generalized additive models, and mixed models.
There will be no hands-on computer exercises, but we will supply a CD with software, example data and demonstration scripts for S-Plus (or R freeware) and Matlab. Their use will be illustrated during the course. After taking this course one will be able to go home to analyze his/her own data.
A background in multiple regression and familiarity with basic matrix operations is needed.
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= Applied Session,
= Theme Session,
= Presenter