Mean Testing under Truncation beyond Gaussian
arXiv:2605.01335v1 Announce Type: new Abstract: We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(cdot mid S)$ for an unknown truncation set $S$ that may hide up to an $varepsilon$-fraction of the probability mass. For distributions with $p$-th directional moments of magnitude at most $nu_{P,p}$, truncation induces a bias of order $O(nu_{P,p}varepsilon^{1-1/p})$. This bias creates a sharp information-theoretic detectability floor: when the signal $alpha$ falls below this […]