Lower Bound Estimation for A Family of High-dimensional Sparse Covariance Matrices

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2023-09-23 DOI:10.1142/s0219691323500455

Huimin Li, Youming Liu

引用次数: 0

Abstract

Lower bound estimation plays an important role for establishing the minimax risk. A key step in lower bound estimation is deriving a lower bound of the affinity between two probability measures. This paper provides a simple method to estimate the affinity between mixture probability measures. Then we apply the lower bound of the affinity to establish the minimax lower bound for a family of sparse covariance matrices, which contains Cai–Ren–Zhou’s theorem in [T. Cai, Z. Ren and H. Zhou, Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation, Electron. J. Stat. 10(1) (2016) 1–59] as a special example.

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一类高维稀疏协方差矩阵的下界估计

下界估计对于最大最小风险的确定起着重要的作用。下界估计的一个关键步骤是推导两个概率测度之间的亲和力的下界。本文提供了一种估计混合概率测度间亲和力的简单方法。在此基础上，利用亲和力的下界建立了一类稀疏协方差矩阵的极大极小下界，该矩阵包含[T]中的周蔡仁定理。J. Stat. 10(1)(2016) 1 - 59]作为特例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.