Semiparametric Modeling, Penalized Splines, and Mixed Models

David Ruppert & Andrew Schultz, Jr
Engineering Department
Cornell University
Wednesday, 21 January 2004
3:10 PM
E202 Engineering Building

A semiparametric models combines parametric and nonparametric components, where the later are functions whose shapes are not confined to a low-dimensional family.  Penalized splines model these nonparametric components using a fixed, pre-determined basis.  Overfitting is prevented by a roughness penalty, and penalized splines include classical smoothing splines as a special case.  A penalized splines can be viewed as a BLUP in a mixed model or as an empirical Bayes estimator.  The mixed mixed viewpoint is especially convenient for applications because of its conceptual simplicity and because it allows use of readily available software.
Additive models, single-index models, and nonlinear regression models can be fit relatively simply.  Penalized spline methods are the most effective methods known for nonparametric regression with covariate measurement errors.  Penalized splines are very effective for nonparametric random effects models, e.g., longitudinal data where each subject has his/her own curve.

Refreshments will be served at 2:45 p.m. in Room 008 of the Statistics




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