A theoretical study of Stein's covariance estimator

• 成果类型: Article
• 署名作者: Rajaratnam, Bala; Vincenzi, Dario
• 署名单位: Stanford University; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw030
• 发表日期: 2016
• 页码: 653666
• 关键词: Matrices; models

摘要

Stein proposed an estimator to address the poor performance of the sample covariance matrix for samples of small size. The estimator does not impose sparsity conditions and uses an isotonizing algorithm to preserve the order of the sample eigenvalues. Despite its superior numerical performance, its theoretical properties are not well understood. We demonstrate that Stein's covariance estimator gives modest risk reductions when it is not isotonized, and when it is isotonized the risk reductions are significant. Three broad regimes of the estimator's behaviour are identified.