Estimating statistical characteristics under interval uncertainty and constraints: Mean, variance, covariance, and correlation
Year: 2011
Type: article
Abstract: In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, …, xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation. The values xi come from measurements, and measurement is never absolutely accurate. Often, the only information that we have about the measurement error is the upper bound Δ i on this error. In this case, once we have the measurement result x˜i, the condition :x˜ i – xi: ≤ Δ i implies that the actual (unknown) value xi belongs to the interval xi [special characters omitted] [x˜i – Δ i, x˜i + Δ i]. Different values xi ∈ xi from the corresponding intervals lead, in general, to different values of sample mean, sample variance, etc. It is therefore desirable to find the range of possible values of these characteristics when xi ∈ xi. It is known that evaluating such ranges is, in general, NP-hard. The main objective of this thesis is to design feasible (i.e., polynomial-time) algorithms for practically important situations. Several such algorithms are described and proved to be correct.
Author: Ali Jalal-Kamali
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W99212099