A new statistical test for distinguishing 2-partitions of a finite set

Q4 Mathematics

Model Assisted Statistics and Applications Pub Date : 2022-08-26 DOI:10.3233/mas-221352

S. Dronov

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Abstract

This paper considers a family of so-called 2-partitions of some finite set. Each of them divides the set under study into two disjoint parts. Under the assumption that two such partitions are chosen randomly, the exact probability distribution of the special cluster metric on this family is found. On this basis, a new statistical test for checking the significance of differences between 2-partitions is proposed. In addition, the distribution of the values of this metric is found for the case when both partitions are of the ledge type in ordering the set of objects in ascending order of values of some numerical indicator. This means that one of the parts of each partition, which in some sense is the main one, is a segment. The boundaries of such a segment are called normative. By comparing various estimates of the normative boundaries based on sample data, it is introduced the concept of indicative certainty of the numerical indicator. It can be regarded as the degree of confidence in this indicator as a basis for decision whether an object belongs to the main set of the ledge partition. Some application of the results to medical data processing is considered.

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判别有限集2-分区的一个新的统计检验

本文研究了一类有限集的2分割族。每一种方法都将所研究的集合分成两个互不关联的部分。在随机选择两个这样的分区的假设下，找到了这个族的特殊聚类度量的精确概率分布。在此基础上，提出了一种新的检验2分区间差异显著性的统计检验方法。此外，当两个分区均为窗台类型时，将某数值指示值按升序排列对象集，得到了该度量值的分布。这意味着每个分区的一个部分(在某种意义上是主要部分)是一个段。这样的段的边界称为规范的。通过比较基于样本数据的各种规范边界估计，引入数值指标指示性确定性的概念。它可以看作是该指标的置信度，是判断一个对象是否属于窗台分区主集的依据。研究结果在医疗数据处理中的一些应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Model Assisted Statistics and Applications Mathematics-Applied Mathematics

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Model Assisted Statistics and Applications is a peer reviewed international journal. Model Assisted Statistics means an improvement of inference and analysis by use of correlated information, or an underlying theoretical or design model. This might be the design, adjustment, estimation, or analytical phase of statistical project. This information may be survey generated or coming from an independent source. Original papers in the field of sampling theory, econometrics, time-series, design of experiments, and multivariate analysis will be preferred. Papers of both applied and theoretical topics are acceptable.