超高维精确矩阵估算新方法

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2024-02-28 DOI:10.1016/j.jspi.2024.106164

Wanfeng Liang , Yuhao Zhang , Jiyang Wang , Yue Wu , Xiaoyan Ma

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引用次数: 0

摘要

修正的乔尔斯基分解（MCD）方法通常用于精度矩阵估计，假设随机变量具有特定的阶次。本文以 MCD 为基础，针对超高维精度矩阵开发了一种不依赖变量阶数的基于置换的重新拟合交叉验证（PRCV）估计程序。在无正态分布假设的弗罗贝尼斯规范下，建立了所提出估计器的一致性。仿真研究表明，该方法在各种情况下都有令人满意的表现。提出的方法还被用于分析真实数据。我们在 https://github.com/lwfwhunanhero/PRCV 网站上提供了完整的代码。

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A new approach for ultrahigh dimensional precision matrix estimation

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.

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.