Category: Statistics

Summary: Testing whether clipping heavy-tailed covariance entries suppresses false spectral spikes at low correlation but harms alignment when real block structure is strong.

Heavy-tailed covariance data can generate spurious large eigenvalues that look like real structure, and clipping extreme values is a natural fix. This experiment asks whether that fix has a tradeoff: helping when block correlation is weak while damaging genuine signal recovery when the underlying block structure is strong.

The script sweeps Student-t tail parameter, block correlation, and clipping level, then measures top eigenvalues, false spike excess, and alignment of the leading eigenvector with the planted structure. Contrasts between clipped and unclipped runs are used to test whether moderate winsorization helps in one regime but hurts in another.

That makes the problem more subtle than asking whether clipping is good on average. The value lies in mapping the regime dependence of spectral cleaning in heavy-tailed settings, where the same intervention may suppress artifacts and erase signal depending on correlation strength.

Method: Repeated heavy-tailed block-covariance simulations over tail index, correlation, and clipping level, with spectral and alignment contrasts between clipped and unclipped runs.

What is measured: Top eigenvalues, false spike excess, eigenvector alignment, contrasts between clip levels, and hypothesis signals for low-correlation benefit versus high-correlation damage.