Yale University
Department of Statistics

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.