Statistical Hypothesis Testing under Interval Uncertainty: An Overview

Vladik Kreinovich ； Hung T. Nguyen ； Sa-Aat Niwitpong

《International Journal of Intelligent Technologies and Applied Statistics》 1卷1期 (2008/03) Pp. 1-32

https://doi.org/10.6148/IJITAS.2008.0101.01

並列摘要

An important part of statistical data analysis is hypothesis testing. For example, we know the probability distribution of the characteristics corresponding to a certain disease, we have the values of the characteristics describing a patient, and we must make a conclusion whether this patient has this disease. Traditional hypothesis testing techniques are based on the assumption that we know the exact values of the characteristic (s) x describing a patient. In practice, the value comes from measurements and is, thus, only known with uncertainty: x≠x In many practical situations, we only know the upper bound on the (absolute value of the) measurement error △x(superscript def)(the symbol is abbreviated)x=x-x. In such situation, after the measurement, the only information that we have about the (unknown) value x of this characteristic is that x belongs to the interval [(x-△, x + △].
In this paper, we overview different approaches on how to test a hypothesis tinder such interval uncertainty. This overview is based on a general approach to decision making under interval uncertainty, approach developed by the 2007 Nobelist L. Hurwicz.

並列關鍵字

Statistical hypothesis testing ； Interval uncertainty ； Hurwicz criterion