Universal rank inference via residual subsampling with application to large networks
提出一种基于残差子抽样的通用秩推断方法，适用于低秩加噪声模型，包括多种网络模型，通过构造检验统计量来检验和估计矩阵秩，理论证明其有效性。
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.