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Statistica Sinica 30 (2020), 1027-1048

ON AGGREGATE DIMENSION REDUCTION
Qin Wang, Xiangrong Yin, Bing Li and Zhihui Tang
The University of Alabama, University of Kentucky
Penn State University and PPDI

Abstract: We propose a dimension-reduction method based on the aggregation of localized estimators. The dual process of localization and aggregation helps to mitigate the bias due to the symmetry in the predictor distribution, and achieves exhaustive estimation of the dimension-reduction space. This approach does not involve numerical optimization or the inversion of large matrices, resulting in a fast and stable algorithm suited for processing large, high-dimensional data sets. We demonstrate the efficacy of our method via simulation and real-data applications.

Key words and phrases: Central subspace, k-nearest neighbor, sliced inverse regression.

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