American Statistical Association
New York City
Metropolitan Area Chapter

Mailman School of Public Health
Columbia University
Department of Biostatistics Colloquium



PENALIZED SPLINES, MIXED MODELS, AND RECENT LARGE-SAMPLE RESULTS

by

Prof. David Ruppert
School of Operations Research and Information Engineering
Cornell University


Abstract

A semiparametric regression models combines parametric and nonparametric components. Penalized splines can model the nonparametric components using a pre-determined basis that is rich enough to avoid under-fitting. Over-fitting 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 model viewpoint is especially convenient for applications because of its conceptual simplicity, because it allows the use of readily available software, and especially because it can incorporate random subject-specific effects as well. The first part of this talk will be an overview of mixed-model splines for semiparametric regression circa 2003 when “Semiparametric Regression” was published by Ruppert, Wand, and Carroll. Several case studies will be presented.

The second half will survey recent work on the asymptotic theory of penalized splines. 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 increase sufficiently fast that it does not play the role of a smoothing parameter. 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.


Date: Thursday, May 7, 2009
Time: 4:00 - 5:00 P.M.
Location: Mailman School of Public Health
Department of Biostatistics
722 West 168th Street
Biostatistics Computer Lab
6th Floor - Room 656
New York, New York

RESERVATIONS ARE NOT REQUIRED

Refreshments will be served at 3:30 P.M. in the
Biostatistics Conference Room (R627).


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