数学
残余物
检验统计量
秩(图论)
推论
统计的
特征向量
应用数学
统计假设检验
无效假设
基质(化学分析)
算法
统计
组合数学
人工智能
计算机科学
材料科学
量子力学
复合材料
物理
作者
Han Xiao,Qing Yang,Yingying Fan
摘要
Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic via subsampling entries of the residual matrix after extracting the spiked components. The test statistic converges in distribution to the standard normal under the null hypothesis, and diverges to infinity with asymptotic probability one under the alternative hypothesis. The effectiveness of RIRS procedure is justified theoretically, utilizing the asymptotic expansions of eigenvectors and eigenvalues for large random matrices recently developed in (J. Amer. Statist. Assoc. 117 (2022) 996–1009) and (J. R. Stat. Soc. Ser. B. Stat. Methodol. 84 (2022) 630–653). The advantages of the newly suggested procedure are demonstrated through several simulation and real data examples.
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