Fused Estimators of the Central Subspace in Sufficient Dimension Reduction

• Activity Number: 296
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Xin Zhang*+ and Dennis Cook
• Companies: University of Minnesota-Twin Cities and University of Minnesota
• Keywords: central subspace ; inverse regression estimation ; sliced inverse regression ; sufficient dimension reduction

Abstract

When studying the regression of a univariate variable Y on a vector X of predictors, most existing sufficient dimension reduction (SDR) methods require the construction of slices of Y in order to estimates moments of the conditional distribution of X given Y . But there is no widely accepted method for choosing the number of slices, while a poorly chosen slicing scheme may produce miserable results. We propose a novel and easily implemented fusing method that can mitigate the problem of choosing a slicing scheme and improve estimation efficiency at the same time. We develop two fused estimators - called FIRE and DIRE - based on an optimal inverse regression estimator. The asymptotic variances of the fused estimators are no larger than that of the original methods regardless of the choice of slicing scheme. Simulation studies show that the fused estimators perform effectively the same as or substantially better than the parent methods. Fused estimators based on other methods can be developed in parallel: Fused SIR and fused CSS-SIR are introduced briefly. Simulation studies of the fused CSS-SIR estimator show substantial gain over CSS-SIR.