Computing Statistics under Interval Uncertainty: Case of Relative Accuracy

Abstract

Formulation of the problem. In the previous chapters, we have shown that for many statistical characteristics C, computing them with a given absolute accuracy ε – i.e., computing a value $\tilde{C}$ for which |$\tilde{C}$ – C| ≤ ε is NP-hard.

It turns out that if we are interested in computing these characteristics with relative accuracy – relative with respect to, e.g., the largest of the inputs – then it often possible to estimate these characteristics in polynomial time. These results first appeared in [57, 176].