After presenting a short review of random-projection techniques, we address two important statistical problems: that of estimating for mixtures of multivariate normal distributions and mixtures of $t$-distributions based of univariate projections, and that of measuring the agreement between two different random partitions. The results are based on an earlier work of the authors, where 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. 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：在简要回顾随机投影技术后，我们探讨了两个重要的统计问题：基于单变量投影的多元正态分布混合与$t$分布混合的估计问题，以及两种不同随机划分之间一致性的度量问题。这些结果建立在作者早期研究的基础上，该研究表明多元高斯或$t$分布混合可以通过投影到特定预定有限直线集进行区分，直线数量仅取决于所涉及分布的总数和环境维度。我们还将所提方法与期望最大化方法EM的稳健版本进行比较。针对每个问题，我们给出了实现任务的算法，并通过模拟实验与现有方法进行了对比。