TY - JOUR
AB - In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.
AU - Ding, Xiucai
AU - Ji, Hong Chang
ID - 14780
JF - Stochastic Processes and their Applications
KW - Applied Mathematics
KW - Modeling and Simulation
KW - Statistics and Probability
SN - 0304-4149
TI - Spiked multiplicative random matrices and principal components
VL - 163
ER -