How to measure if a distribution has light tails?

The sub-Gaussian parameter measures how quickly a distribution's tails decay—crucial for understanding data from normal-like populations. This work proposes a practical estimator via empirical optimization and proves it converges at rate 1/√n when tails are sufficiently regular, with minimax-optimal guarantees. Applied to genomics, it outperforms existing methods for large-scale permutation tests in genome-wide enrichment studies.