How to Find the Dependence Based on Measurements with Unknown Accuracy: Towards a Theoretical Justification for Midpoint and Convex-Combination Interval Techniques and Their Generalizations

Abstract

In practice, we often need to find regression parameters in situations when for some of the values, we have several results of measuring this same value. If we know the accuracy of each of these measurements, then we can use the usual statistical techniques to combine the measurement results into a single estimate for the corresponding value. In some cases, however, we do not know these accuracies, so what can we do? In this paper, we describe two natural approaches to solving this problem. In addition to describing general techniques, our results also provide a theoretical explanation for several semi-heuristic ideas proposed for solving an important particular case of this problem—the case when we deal with interval uncertainty.