High-Dimensional Hettmansperger-Randles Estimator and its Applications

2025/05/03 by Guowei Yan, Long Feng, Yan, Guowei +3 · 1 citation
Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Computer and information sciences #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2505.01669

openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles Estimator for the location parameter and scatter matrix of elliptical distributions in high-dimensional scenarios. Subsequently, we apply these estimators to two prominent problems: the one-sample location test problem and quadratic discriminant analysis. We discover that the corresponding new methods exhibit high effectiveness across a broad range of distributions. Both simulation studies and real-data applications further illustrate the superiority of the newly proposed methods.

Citations

• A Spatial-Sign based Direct Approach for High Dimensional Sparse Quadratic Discriminant Analysis
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• Spatial-Sign based Maxsum Test for High Dimensional Location Parameters
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• An Overview on the Estimation of Large Covariance and Precision Matrices
• Central Limit Theorems and Bootstrap in High Dimensions
• Mean vector testing for high dimensional dependent observations
• Power Enhancement in High Dimensional Cross-Sectional Tests
• Power Enhancement in High-Dimensional Cross-Sectional Tests
• A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation
• Covariance regularization by thresholding
• Regularized estimation of large covariance matrices
• A Distribution-Free M-Estimator of Multivariate Scatter

Cited by

• High dimensional matrix estimation through elliptical factor models

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• Nearly Optimal Robust Covariance and Scatter Matrix Estimation Beyond Gaussians
• Spatial-Sign based High-Dimensional Location Test