This paper develops an outlier detection procedure for multinomial data when the number of categories tends to infinity. Most of the outlier detection methods are based on the assumption that the observations follow multivariate normal distribution, while in many modern applications, the observations either are measured on a discrete scale or naturally have some categorical structures. For such multinomial observations, there are rather limited approaches for outlier detection. To overcome the main obstacle, the least trimmed distances estimator for multinomial data and a fast algorithm to identify the clean subset are introduced in this work. Also, a threshold rule is considered through the asymptotic distribution of measure distance to identify outliers. Furthermore, a one-step reweighting scheme is proposed to improve the efficiency of the procedure. Finally, the finite sample performance of our method is evaluated through simulations and is compared with that of available outlier detection methods.

中文翻译：

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具有大量类别的多项数据的异常值检测

当类别数量趋于无穷大时，本文开发了一种用于多项数据的异常值检测程序。大多数异常值检测方法都基于观测遵循多元正态分布的假设，而在许多现代应用中，观测要么在离散尺度上测量，要么自然具有一些分类结构。对于这种多项式观察，异常值检测的方法相当有限。为了克服主要障碍，在这项工作中引入了多项数据的最小修剪距离估计​​器和识别干净子集的快速算法。此外，通过测量距离的渐近分布考虑阈值规则来识别异常值。此外，提出了一种一步重加权方案以提高程序的效率。最后，通过模拟评估我们方法的有限样本性能，并与可用的异常值检测方法进行比较。