A1062
Title: A penalized least squares approach to adaptive ridge regression
Authors: Keith Knight - University of Toronto (Canada) [presenting]
Abstract: A prior study showed that ridge regression estimates can be viewed as a weighted average of subset least squares estimates, with weights depending only on the design. Using this representation, the total weight that each predictor contributes to a given ridge estimate is computed, thereby defining the notion of partial degrees of freedom for each predictor; the equivalent degrees of freedom are then equal to the sum of the partial degrees of freedom. Thus, by varying the ridge parameters, can define "fractional" model selection where the partial degrees of freedom for each predictor vary between 0 and 1. A penalized least squares approach is considered for estimating the partial degrees of freedom, allowing the estimated partial degrees of freedom to potentially equal 0. Some asymptotic theory of the resulting estimates is also considered.
