A new approach for ultrahigh dimensional precision matrix estimation

被引：2

作者：

Liang, Wanfeng ^{[1
]}

Zhang, Yuhao ^{[2
]}

Wang, Jiyang ^{[3
,4
]}

Wu, Yue ^{[3
]}

Ma, Xiaoyan ^{[5
]}

机构：

[1] Dongbei Univ Finance & Econ, Sch Data Sci & Artificial Intelligence, Dalian 116025, Liaoning, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[3] Nankai Univ, Sch Stat & Data Sci, Tianjin 300071, Peoples R China

[4] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 300071, Xinjiang, Peoples R China

[5] Ningxia Univ, Sch Math & Stat, Yinchuan 750021, Ningxia, Peoples R China

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2024年 / 232卷

基金：

中国国家自然科学基金;

关键词：

Modified Cholesky decomposition; Precision matrix; Refitted cross validation; Ultrahigh dimension; COVARIANCE; RATES; CONVERGENCE; SELECTION;

D O I：

10.1016/j.jspi.2024.106164

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The modified Cholesky decomposition (MCD) method is commonly used in precision matrix estimation assuming that the random variables have a specified order. In this paper, we develop a permutation -based refitted cross validation (PRCV) estimation procedure for ultrahigh dimensional precision matrix based on the MCD, which does not rely on the order of variables. The consistency of the proposed estimator is established under the Frobenius norm without normal distribution assumption. Simulation studies present satisfactory performance of in various scenarios. The proposed method is also applied to analyze a real data. We provide the complete code at https://github.com/lwfwhunanhero/PRCV.

引用

页数：12

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