In this paper we study a finite Gaussian mixture model with an additional uniform component that has the role to catch points in the tails of the data distribution. An adaptive constraint enforces a certain level of separation between the Gaussian mixture components and the uniform component representing noise and outliers in the tail of the distribution. The latter makes the proposed tool particularly useful for robust estimation and outlier identification. A constrained ML estimator is introduced for which existence and consistency is shown. One of the attractive features of the methodology is that the noise level is estimated from data. We also develop an EM-type algorithm with proven convergence. Based on numerical evidence we show how the methods developed in this paper are useful for several fundamental data analysis tasks: outlier identification, robust location-scale estimation, clustering, and density estimation.

在本文中，我们研究了具有附加均匀分量的有限高斯混合模型，该分量具有捕捉数据分布尾部中的点的作用。自适应约束在高斯混合分量与表示分布尾部噪声和异常值的均匀分量之间强制实施一定程度的分离。后者使得所提出的工具对于稳健估计和异常值识别特别有用。引入了一个受约束的 ML 估计器，其存在性和一致性被显示出来。该方法的一个吸引人的特点是噪声水平是从数据中估计出来的。我们还开发了一种经过验证的收敛性的 EM 型算法。基于数值证据，我们展示了本文中开发的方法如何用于几个基本的数据分析任务：