On aggregate dimension reduction

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.