Robust Association Studies Using Density Power Divergences with Application to Consumer Expenditure Survey and Survey of Consumer Finance

• Activity Number: 591
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): T N Sriram*+ and Ross Iaci
• Companies: University of Georgia and The College of William and Mary
• Keywords: Multivariate association measures ; Density power divergence ; Density alpha divergence ; Dimension Reduction ; Permutation test ; Robustness

Abstract

In this talk, we will introduce two new families of multivariate association measures based on power divergence and alpha divergence, respectively, that recover both linear and nonlinear relationships between multiple sets of random vectors. Importantly, this novel approach not only characterizes independence, but also provides a smooth bridge between well-known distances that are inherently robust against outliers. Algorithmic approaches are developed for dimension reduction and selection of the optimal robust association index. Extensive simulation studies are performed to assess the robustness of these association measures under different types and proportions of contamination. We illustrate the usefulness of our methods in application by analyzing two socioeconomic data sets that are known to contain outliers or extreme observations. Some theoretical properties, including the consistency of the estimated coefficient vectors, are investigated and computationally efficient algorithms for our nonparametric methods are provided.