 Minimax rates of convergence for sliced inverse regression with differential privacyWenbiao Zhao, Xuehu Zhu and Lixing Zhu Computational Statistics & Data Analysis, 2025, vol. 201, issue C Abstract: Sliced inverse regression (SIR) is a highly efficient paradigm used for the purpose of dimension reduction by replacing high-dimensional covariates with a limited number of linear combinations. This paper focuses on the implementation of the classical SIR approach integrated with a Gaussian differential privacy mechanism to estimate the central space while preserving privacy. We illustrate the tradeoff between statistical accuracy and privacy in sufficient dimension reduction problems under both the classical low- dimensional and modern high-dimensional settings. Additionally, we achieve the minimax rate of the proposed estimator with Gaussian differential privacy constraint and illustrate that this rate is also optimal for multiple index models with bounded dimension of the central space. Extensive numerical studies on synthetic data sets are conducted to assess the effectiveness of the proposed technique in finite sample scenarios, and a real data analysis is presented to showcase its practical application. Keywords: Sliced inverse regression; Differential privacy; Minimax rate (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:201:y:2025:i:c:s0167947324001257 DOI: 10.1016/j.csda.2024.108041 Access Statistics for this article Computational Statistics & Data Analysis is currently edited by S.P. Azen More articles in Computational Statistics & Data Analysis from Elsevier |
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