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February 2020 Sparse SIR: Optimal rates and adaptive estimation
Kai Tan, Lei Shi, Zhou Yu
Ann. Statist. 48(1): 64-85 (February 2020). DOI: 10.1214/18-AOS1791

Abstract

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.

Citation

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Kai Tan. Lei Shi. Zhou Yu. "Sparse SIR: Optimal rates and adaptive estimation." Ann. Statist. 48 (1) 64 - 85, February 2020. https://doi.org/10.1214/18-AOS1791

Information

Received: 1 April 2018; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196530
MathSciNet: MR4065153
Digital Object Identifier: 10.1214/18-AOS1791

Subjects:
Primary: 62H12
Secondary: 62G08, 62G09

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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