We consider Frechet sufficient dimension reduction with responses being complex random objects in a metric space and high-dimensional Euclidean predictors. We propose a novel approach, called the weighted inverse regression ensemble method, for linear Frechet sufficient dimension reduction. The method is further generalized as a new operator defined on reproducing kernel Hilbert spaces for nonlinear Frechet sufficient dimension reduction. We provide theoretical guarantees for the new method via asymptotic analysis. Intensive simulation studies verify the performance of our proposals, and we apply our methods to analyse handwritten digit data and real-world affective face data to demonstrate its use in real applications.
Publication:
Biometrika, 2022,109,4,975-992
Author:
Ying, Chao,
School of Statistics, Key Lab Adv Theory & Applicat Stat & Data Sci MOE，East China Normal University, Shanghai 200062, China
Yu, Zhou,
School of Statistics, Key Lab Adv Theory & Applicat Stat & Data Sci MOE，East China Normal University, Shanghai 200062, China
Email: zyu@jiafengwangluo.com