Department of Statistical Science
Duke University

presents:

Charles Kooperberg
University of Washington

"The Use of Polynomial Splines and Their Tensor Products
in Functional Modeling"

Abstract:

- density estimation;
- regression;
- survival analysis (hazard regression);
- time series data, where we want to estimate the spectral distribution;
- polychotomous regression and multiple classification.

In solving these and many other problems, the traditional and well studied way in statistics is to assume a parametric model, after which parameters are estimated and inferences about the models are made.'

An alternative approach is to use polynomial splines and selected tensor products. Using polynomial splines, an unknown function is modeled to be in a linear space. Stepwise algorithms make it possible to determine this space adaptively. Polynomial spline methodologies include LOGSPLINE (density estimation), MARS (regression), HARE (hazard regression), POLYCLASS (polychotomous regression and multiple classification) and LSPEC (spectral distribution estimation).

I will give an introduction to polynomial splines, and how they can be used in functional modeling. Examples that I plan to use will be density estimation and polychotomous regression.

Friday, March 29, 1996

11:45 am - 12:45 pm

130 Sociology/Psychology Building