A significant characteristic of fully developed turbulence is scale invariance, i.e., in a wide range of scale ratios a, usually known as the inertial range, the moments of order $q > 0$ of the increments of the velocity field $v(x)$ or of the aggregated dissipation field $r (x)$ behave as power laws with respects to scale ratios. A key issue in the analysis of turbulence data lies in accurately and precisely measuring the scaling exponents. This yields two questions: how can efficient estimators for the $ζ(q)$ be defined and what are their statistical performance? While the former question owns classical answers, the latter has been mostly overlooked. In the present work, we address carefully this question.