Tests of rank

Robin & Smith (2000) — tests of rank

Result

rank tests from the smallest estimated characteristic roots of a $\sqrt n$-consistent, asymptotically normal matrix estimate; under rank $r$ the $n$-scaled smallest roots converge to a weighted sum of independent $\chi^2$ variables.

Use

the trace-form kin of O7.4(b): there the $n^{d-r}$-scaled determinant of the empirical binned information converges to $\det A\,\det(WP^{-1}W^\top)/\det V$ with $W$ a linear image of independent Gaussians — a determinant instead of a trace, an uncentred fixed-partition Gram matrix instead of a regression coefficient matrix, and no test is built.

Verification

abstract verified (AUDIT-RETENTION-PLUGIN-VECTOR, 6 Sep 2026); theorem numbering not read.