On Efficient Dimension Reduction with Respect to a Statistical Functional of Interest

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wei Luo*+ and Bing Li and Xiangrong Yin
• Companies: Pennsylvania State University and The Pennsylvania State University and University of Georgia
• Keywords: Central subspace ; Conditional mean, variance and quantile ; Efficient information ; Efficient score ; Frechet derivative and its representation ; Projection

Abstract

We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance, and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the linear functional, the composite linear functional, and the implicit functional. In conjunction with our theoretical analysis, we also propose a class of one-step Newton-Raphson estimators and show by simulation that they substantially outperform existing methods. Finally, we apply the new method to construct the central mean and central variance subspaces for a data set of the physical measurements and age of abalones, which exhibits a strong pattern of heteroscedasticity.