Estimating Mean and Variance under Interval Uncertainty: Dynamic Case
Rafik Aziz Aliev, Владик Крейнович · scholarworks - UTEP (The University of Texas at El Paso) · 2011
In many practical situations, it is important to estimate the mean E and the variance V from the sample values x1,..., xn. Usually, in statistics, we consider the case when the parameters like E and V do not change with time and when the sample values xi are known exactly. In practice, the values xi come from measurements, and measurements are never 100 % accurate. In many cases, we only know the upper bound ∆i on the measurement error. In this case, once we know the measured value ˜xi, we can conclude that the actual (unknown) value xi belongs to the interval [˜xi − ∆i, ˜xi + ∆i]. Different values xi from these intervals lead, in general, to different values of E and V. It is therefore desirable to find the ranges E and V of all possible values of E and V. While this problem is, in general, NP-hard, in many practical situations, there exist efficient algorithms for computing such ranges. In practice, processes are dynamic. As a result, reasonable estimates for E and V assign more weight to more recent measurements and less weight to the past ones. In this paper, we extend known algorithms for computing the ranges E and V to such dynamic estimates. 1