A shrinkage estimation for large dimensional precision matrices using random matrix theory

2012/11/11 by Cheng Wang, Wang, Cheng, Guangming Pan +3
Environmental Science · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Random Matrices and Applications #Soil Geostatistics and Mapping #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1211.2400

openalex publication_date 2012/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were also conducted based on the asymptotic results deriving from random matrix theories. The new estimator which has a simple explicit formula is distribution-free and applicable to situation where the dimension of observation is greater than the sample size. Further, no assumptions are required on the structure of the population covariance matrix or the precision matrix. Finally, numerical studies are conducted to examine the performances of the new estimator and existing methods for a wide range of settings.

Citations

• Optimal feature selection for sparse linear discriminant analysis and its applications in gene expression data
• Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices
• A well-conditioned estimator for large-dimensional covariance matrices

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