Statistics and Data Science Seminar
Prof. Lan Xue
Oregon State University
Consistent variable selection in additive models
Abstract: We propose a penalized polynomial spline method for
simultaneous model estimation and variable selection in additive models. It
approximates nonparametric functions by polynomial splines, and
minimizes the sum of squared errors subject to an additive penalty on norms
of spline functions. This approach sets estimators of certain function
components to zero, thus performing variable selection. Under mild
conditions, we show that the newly proposed method estimates the non-zero
function components in the model with the same optimal mean square
convergence rate as the standard polynomial spline estimators, and correctly
sets the zero function components to zero with probability approaching one,
as $n$ goes to infinity. Besides being theoretically justified, the proposed
method is easy to understand and straightforward to implement. Extensive
Monte Carlo simulation studies show the newly proposed method compares
favorably with the existing ones in finite sample performance. We also
illustrate the use of the proposed method by analyzing two data sets.
Wednesday September 2, 2009 at 3:00 PM in SEO 636