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Activity Number: 186 - Contributed Poster Presentations: International Chinese Statistical Association
Type: Contributed
Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
Sponsor: International Chinese Statistical Association
Abstract #303090
Title: Sparse SIR: Optimal Rates and Adaptive Estimation
Author(s): Kai Tan*
Keywords: Sliced inverse regression; Sufficient Dimension Reduction; Sparsity

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.

Authors who are presenting talks have a * after their name.

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