A note on cyclic shift permutation testing for large eigenvalues

Abstract

Recent publications have described the problem of testing for the “significance” of large sample (empirical) matrix eigenvalues in the presence of modest variation of underlying true eigenvalues. This modest variation often can be ascribed to endemic dependence in one matrix dimension (e.g., rows), whereas the null hypothesis concerns the other dimension (columns). The need for such testing frequently arises in genomics, time‐series analysis, and a variety of other fields. However, the tools available for testing are underdeveloped, with statistical properties that may be sensitive to the true eigenvalues. The purpose of this note is to point the reader to this emerging literature and to suggest that the tool of cyclic shift permutation may be well‐suited to the problem.