ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS, .
ON IDENTIFIABILITY OF MIXTURES OF INDEPENDENT DISTRIBUTION LAWS, .
复制标题
关于独立分布定律混合物的可识别性，。
DOI：
10.1051/ps/2011166
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Yashin,Anatoliy
中科院分区：
文献类型：
--
作者：
Kovtun,Mikhail;Akushevich,Igor;Yashin,Anatoliy
我们考虑一类分类随机变量的联合分布律的表示（即，多变量分类变量）作为独立分布律（即随机变量相互独立的分布律）的混合。对于随机变量的无限族，我们描述了一类具有可识别混合测度的混合变量。从实用的角度来看，这门课也很有趣，因为它的结构阐明了选择一个“好”的有限随机变量族用于应用研究的原则。对于随机变量的有限族，混合测度永远是不可识别的;然而，它总是拥有许多可识别的不变量，这些不变量提供了关于所考虑的分布的大量信息。
We consider representations of a joint distribution law of a family of categorical random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e. distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting a “good” finite family of random variables to be used in applied research. For finite families of random variables, the mixing measure is never identifiable; however, it always possesses a number of identifiable invariants, which provide substantial information regarding the distribution under consideration.