Uniform inference under local-to-zero couplings and data-dependent selection

Establish uniform validity of spectral-radius inference for the two-stage spectral estimator over local-to-zero coupling sequences when support selection is data-dependent, including the fixed-alpha screening rule used by the monitoring algorithm.

Background

The paper proves bootstrap validity only under consistent support selection, a locally smooth fixed-point inversion, and a simple Perron root. Those conditions exclude the fixed-alpha screening rule used in the implemented algorithm, because null entries continue to be selected with nonvanishing probability.

The unresolved issue is a uniform selective-inference theory covering local-to-zero couplings, where support-selection randomness does not disappear asymptotically. Such a result would bridge the gap between the pointwise theorem and the empirical spectral-alarm procedure, whose observed coverage is below the nominal level.

References

A uniform theory over local-to-zero couplings (selective-inference regime) remains open---but it is now the only open layer, and the target of the coverage statement ($\rho{(2)*}$, the pseudo-true spectral radius) is stated explicitly.

— Output-Only Identification and Spectral Monitoring of Coupled Feedback Networks with Known Time-Varying Actuation  (2608.25844 - Woo, 26 Aug 2026) in Section 5, subsection “Uncertainty quantification for spectral alarms,” immediately after Theorem 5 (Bootstrap validity under consistent selection)