Statistical Hypothesis Testing Under Interval Uncertainty: An Overview
Statistical Hypothesis Testing Under Interval Uncertainty: An Overview
复制标题
区间不确定性下的统计假设检验：概述
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. Niwitpong
中科院分区：
文献类型：
--
作者：
V. Kreinovich;H. Nguyen;S. Niwitpong
统计数据分析的一个重要部分是假设检验。例如，我们知道了某种疾病对应的特征的概率分布，我们有了描述一个病人的特征的值，我们必须得出这个病人是否患有这种疾病的结论。传统的假设检验技术是基于这样的假设：我们知道描述一个病人的特征x的确切值。在实际中，值x来自于测量，因此，只有在不确定的情况下才知道：x 6 x。在许多实际情况下，我们只知道测量误差（绝对值）¢的上界¢def = x i x。在这种情况下，在测量之后，我们对该特性的（未知）值x的唯一信息是x属于区间[x i¢；[+ 1]。在本文中，我们概述了在这种区间不确定性下如何检验假设的不同方法。本综述基于区间不确定性下决策的一般方法，该方法由2007年诺贝尔奖获得者L. Hurwicz开发。
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 x comes from measurements and is, thus, only known with uncertainty: x 6 x. In many practical situations, we only know the upper bound ¢ on the (absolute value of the) measurement error ¢x def = x i 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 i ¢; x + ¢]. In this paper, we overview difierent approaches on how to test a hypothesis under 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.