In an earlier work arXiv:2410.22038, it was shown that mixtures of multivariate Gaussian or $t$-distributions can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending only on the total number of distributions involved and on the ambient dimension. Using this work, we address the following two important statistical problems: that of testing and measuring the agreement between two different random partitions, and that of estimating for mixtures of multivariate normal distributions and mixtures of $t$-distributions based of univariate projections. We also compare our proposal with robust versions of the expectation-maximization method EM. In each case, we present algorithms for effecting the task, and compare them with existing methods by carrying out some simulations.

翻译：在先前的工作arXiv:2410.22038中，已证明多元高斯分布或$t$分布的混合可以通过将其投影到一组特定的预定有限直线集上来区分，所需直线数量仅取决于所涉分布总数与环境维度。基于此项工作，我们解决了以下两个重要统计问题：测试与度量两个不同随机划分之间的一致性，以及基于单变量投影估计多元正态分布混合与$t$分布混合。我们还将所提方法与期望最大化方法EM的鲁棒版本进行比较。针对每个问题，我们提出了实现任务的算法，并通过模拟实验与现有方法进行对比。