Year: 2025
Type: article
Abstract: In this paper, we investigate the global spectral properties of the sample canonical correlation (SCC) matrix under the alternative hypothesis to provide a more comprehensive description of the association between two sets of variables. Our research involves establishing the relationship between the eigenvalues of the SCC matrix and that of the block correlation matrix, as well as proving the universality of the limiting spectral distribution (LSD) of the block correlation matrix. By combining the results from the normal case, we establish the limiting spectral distribution (LSD) of the SCC matrix with a general underlying distribution under the arbitrary rank alternative hypothesis. Finally, we present several simulation examples and find that they fit well with our theoretical results.
Author: Xiaozhuo Zhang
Institution: Northeast Normal University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408919490