Using Generalized Correlation to Affect Variable Selection in Very High-Dimensional Problems

• Activity Number: 48
• Type: Invited
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: JCGS-Journal of Computational and Graphical Statistics
• Author(s): Hugh Miller*+ and Peter Hall
• Companies: The University of Melbourne and The University of Melbourne
• Keywords: Bootstrap ; Generalized correlation ; Hidden explanatory variables ; Instrumental variables ; Linear models

Abstract

Using the traditional linear model to implement variable selection can perform effectively in some cases, provided the response to relevant components is approximately monotone and its gradient changes only slowly. In other circumstances, nonlinearity of the response can result in signi?cant vector components being overlooked. Even if good results are obtained by linear model ?tting, they can sometimes be bettered by using a nonlinear approach. These circumstances can arise in real data situations. We suggest an approach based on ranking generalized empirical correlations between the response variable and components of the explanatory vector, as well as a bootstrap method for assessing reliability. The technique is not prediction-based, and can identify variables that are in?uential but not explicitly part of a predictive model. The talk will cover both theoretical and numerical results.