{"ID":6023622,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T15:00:13.465917457Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.06373","arxiv_id":"2607.06373","title":"Error Propagation in Spectral Functionals of Shrinkage Covariance Estimators: Perturbation Bounds and Calibrated Inference","abstract":"Rolling covariance estimates feed two objects that are routinely treated as market structure. The first is the dominant eigenspace, monitored through the projector movement $\\widehat D_{K,t}=\\|\\widehat P_{K,t}-\\widehat P_{K,t-1}\\|_F$; the second comprises scalar spectral functionals such as the absorption ratio and the leading-eigenvalue share. Both fluctuate under estimation noise, and shrinkage changes the law of that noise, so reading their movements as structural change requires calibration. For the eigenspace, we derive a first-order null law for $\\widehat D_{K,t}$ between overlapping windows that share most of their data and show that it transfers without change to rotation-equivariant shrinkage estimators. A distribution-free Davis-Kahan band gauges whether the eigenspace is identified, an estimator-aware bootstrap provides the calibrated test, and a companion power analysis gives an approximate design rule for the smallest detectable rotation. For the scalar functionals, we show that first-order immunity to elliptical kurtosis holds for scale-invariant functionals and only for them, so that one estimated scalar calibrates the projector null and the absorption-ratio and leading-share intervals across the elliptical family. In high dimensions, where shrinkage cleaning biases the absorption ratio, we give a trace-preserving spike-debiased estimator that removes the bias. The results are verified by simulation under a known population covariance; an equity-panel appendix shows the procedures as diagnostics when the population is unknown.","short_abstract":"Rolling covariance estimates feed two objects that are routinely treated as market structure. The first is the dominant eigenspace, monitored through the projector movement $\\widehat D_{K,t}=\\|\\widehat P_{K,t}-\\widehat P_{K,t-1}\\|_F$; the second comprises scalar spectral functionals such as the absorption ratio and the...","url_abs":"https://arxiv.org/abs/2607.06373","url_pdf":"https://arxiv.org/pdf/2607.06373v1","authors":"[\"Ahmad Koman\"]","published":"2026-07-07T15:11:16Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\",\"q-fin.ST\",\"stat.CO\"]","methods":"[]","has_code":false}