Hypothesis testing on invariant subspaces of non-symmetric matrices with applications to network statistics

Code

• github.com/jsimons8/networkmodelssubspaces
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Abstract

We extend the inference procedure for eigenvectors of Tyler (1981), which assumes symmetrizable matrices to generic invariant and singular subspaces of non-diagonalisable matrices to test whether R^p r is an element of an invariant subspace of M R^p p. Our results include a Wald test for full-vector hypotheses and a t-test for coefficient-wise hypotheses. We employ perturbation expansions of invariant subspaces from Sun (1991) and singular subspaces from Liu et al. (2007). Based on the former, we extend the popular Davis-Kahan bound to estimations of its higher-order polynomials and study how the bound simplifies for eigenspaces but attains complexity for generic invariant subspaces.

Reproductions