This paper deals with the problem of testing for equality between the location parameters of two unknown symmetric distributions that may belong to different families. Under this framework, we develop a new robust extension of the two-sample Hotelling test (HT). The proposed extension, called measure-transformed HT (MT-HT), operates by applying a transform to the probability measures of some reshaped versions of the two compared data sets. The considered measure transform is structured by a non-negative function, called MT-function, that weights the data points. In the paper we show that proper selection of the involved MT-functions can result in significant enhancement of the decision performance in the presence of non-Gaussian distributions with heavy tails. The advantages of the proposed MT-HT are illustrated in simulation studies that involve synthetic measurements. Additionally, the MT-HT is illustrated for anomaly detection in a blurred and noisy video stream.

中文翻译：

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通过概率测度变换进行稳健的双样本位置测试


本文讨论了测试可能属于不同族的两个未知对称分布的位置参数之间的相等性的问题。在此框架下，我们开发了两个样本霍特林检验（HT）的新的稳健扩展。所提出的扩展称为测量变换 HT (MT-HT)，通过对两个比较数据集的某些重塑版本的概率测量应用变换来进行操作。所考虑的测量变换由非负函数（称为 MT 函数）构成，该函数对数据点进行加权。在本文中，我们表明，在存在重尾非高斯分布的情况下，正确选择所涉及的 MT 函数可以显着提高决策性能。所提出的 MT-HT 的优点在涉及综合测量的模拟研究中得到了说明。此外，MT-HT 还用于模糊和嘈杂的视频流中的异常检测。