### Yale University

Department of Statistics

Seminar

#### Monday, November 13, 1995

Professor
Charles Kooperberg

University of Washington Department of Statistics

#### Joint work with:

Mark Hansen

AT&T Bell Laboratories

Charles
J. Stone

University of California

Young K. Truong

University of North Carolina

#### "The use of polynomial splines and their tensor products in functional
modeling."

Seminar to be held in Room 107, 24 Hillhouse Ave at 4:15 pm

Charles Kooperberg
There numerous situations in which observed data is
generated by some (unknown) mechanism, where interest lies in estimating a
function that is related to a model for the data. Examples include -
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. I will give illustrations based on LOGSPLINE and
POLYCLASS.