How Accurately Can We Determine the Coefficients: Case of Interval Uncertainty

Abstract

In many practical situations, we need to estimate the parameters of a linear (or more general) dependence based on measurement results. To do that, it is useful, before we start the actual measurements, to estimate how accurately we can, in principle, determine the desired coefficients: If the resulting accuracy is not sufficient, then we should not waste time trying and resources and instead, we should invest in more accurate measuring instruments. This is the problem that we analyze in this paper.