David Ruppert is Andrew Schulz Jr. Professor of Engineering, School of Operations Research and Information Engineering, and Professor of Statistical Science, Cornell University. He received a BA in Mathematics from Cornell University in 1970, an MA in Mathematics from the University of Vermont in 1973, and a PhD in Statistics and Probability from Michigan State University in 1977. He was Assistant and then Associate Professor of Statistics at the University of North Carolina, Chapel Hill, from 1977 to 1987. He is a Fellow of the ASA and IMS and received the Wilcoxon Prize in 1986. He has had 23 PhD students, many of them now leading researchers.
Professor Ruppert has worked on stochastic approximation, transformations and weighting in regression, and smoothing. His current research focuses on measurement error models, splines, semiparametric regression, and environmental statistics. He has published over 100 articles in refereed journals and has published several books, Transformation and Weighting in Regression, Measurement Error in Nonlinear Models (first and second editions), Semiparametric Regression, and Statistics and Finance: An Introduction. He is currently working on a second edition to Statistics and Finance.
Abstract
New Results on the Asymptotics of Penalized Splines
The past few years has seen an impressive amount of new work on the asymptotic theory for penalized splines. There have been two parallel developments. In one the number of knots is a smoothing parameter and the asymptotics are similar to those of un-penalized least-squares splines. In the second, the number of knots increases sufficiently fast that it does not play the role of a smoothing parameter. This talk is on the second case and a recently published paper as well as unpublished results will be discussed. In this case, the asymptotics are similar to those of smoothing splines and, somewhat surprisingly, the asymptotic distribution does not depend on the degree of the spline, only the order of the penalty. We show that penalized splines with unequally spaced knots are not design adaptive. A weighted version of penalized splines with equally spaced knots is design adaptive. This is joint work with Yingxing Li and Tanya Apanasovich.