It is shown that some theoretically identifiable parameters cannot be identified from data, meaning that no consistent estimator of them can exist. An important example is a constant correlation between Gaussian observations (in presence of such correlation not even the mean can be identified from data). Identifiability and three versions of distinguishability from data are defined. Two different constant correlations between Gaussian observations cannot even be distinguished from data. A further example are cluster membership parameters in $k$-means clustering. Several existing results in the literature are connected to the new framework.

翻译：事实表明,从数据中无法确定一些理论上可以识别的参数,也就是说,不可能存在这些参数的一致估计数据。一个重要的例子就是高斯观察之间的经常关联(如果存在这种关联,甚至从数据中无法确定平均值)。可识别性和数据与数据区别的三种版本都有定义。高斯观察之间的两种不同的经常关联甚至无法与数据区分。另一个例子是以美元为单位的分组成员参数。文献中的一些现有结果与新框架相关。