Fréchet sufficient dimension reduction for random objects

Some asymptotic theory for the bootstrap

Chao Ying and Zhou Yu

Biometrika, 2022, vol. 109, issue 4, 975-992

Abstract: SummaryWe consider Fréchet 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 Fréchet sufficient dimension reduction. The method is further generalized as a new operator defined on reproducing kernel Hilbert spaces for nonlinear Fréchet 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.

Keywords: Metric space; Sliced inverse regression; Sufficient dimension reduction (search for similar items in EconPapers)
Date: 2022
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