Direction Estimation in Single-Index Models via Distance Covariance

• Activity Number: 75
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wenhui Sheng*+ and Xiangrong Yin
• Companies: and University of Georgia
• Keywords: Brownian Distance Covariance ; Central Subspace ; Distance Covariance ; Single-Index Model ; Sufficient Dimension Reduction

Abstract

We propose a new method for estimating the direction in the single-index model based on distance covariance. The method does not require the existence of any kind of density. And no smoothness is needed in the estimation procedure. It efficiently deals with continuous predictors, a mixture of continuous and categorical predictors, or categorical predictors alone. Asymptotic distribution of the estimate is established. We compare the performance of our method with those of existing methods by simulation and find strong evidence of its advantage over a wide range of models. Our method consistently achieves higher accuracy in our limited simulations. Finally, we apply our method to analyze a data set concerning air pollution. Although we focus on single-index regressions, the underlying idea is applicable more generally.