Asymptotic Theory of Eigenvectors for Random Matrices with Diverging Spikes

• DOI: 10.48550/arxiv.1902.06846
• Publication Date: 2019-01-01
• Authors: Jianqing Fan; Yingying Fan; Xiao Han; Jinchi Lv
• Keywords: Normalization; Asymptotic Analysis; Statistical Inference

Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range statistical applications. To this end, in paper we introduce general framework theory (ATE) spiked with diverging spikes and heterogeneous variances, establish properties eigenvalues scenario generalized Wigner matrix noise. Under some mild regularity conditions, expansions show that they are asymptotically normal after normalization. For eigenvectors, linear combination further it is normalization, where weight vector be arbitrary. We also more using bilinear form. Simulation studies verify validity our new theoretical results. Our family models encompasses many popularly used ones such as stochastic block or without overlapping communities network analysis topic text analysis, exploited inference these large-scale