AI 中文总结
研究多元高斯数据中异常检测，提出新阈值技术，在异常观测稀疏且均值不同、非异常数据均值为零且协方差矩阵未知的假设下，推导相关条件实现渐近精确检测，经模拟和实际数据分析验证性能并与其他方法比较。
AI 中文摘要
本文提出一种新的阈值技术，用于在多元正态随机样本中检测异常。假设异常观测稀疏且均值与其他数据不同，非异常数据均值向量为零，协方差矩阵未知。我们推导了异常观测均值偏移、协方差矩阵及其估计量的条件，在此条件下该方法能实现渐近精确检测，即误分类观测的期望数量随样本量增加趋于零。此外，还确定了任何方法都无法进行精确异常检测的条件。通过广泛的模拟研究说明了该方法的性能，并与其他常用异常检测方法进行了比较。涉及可穿戴活动测量和空气污染时间序列的实际数据分析评估了其在实际环境中的性能。
英文摘要
In this paper, we propose a new thresholding technique for detecting anomalies in multivariate normal random samples, under the assumption that anomalous observations are sparse and differ from the rest of the data in their mean. The mean vector of the non-anomalous data is assumed to be zero, while the covariance matrix is unknown. We derive conditions on the mean shift of the anomalous observations, as well as on the covariance matrix and its estimator, under which the proposed procedure achieves asymptotically exact detection, meaning that the expected number of misclassified observations converges to zero as the sample size increases. In addition, we establish conditions under which exact anomaly detection is impossible for any procedure. The performance of the proposed method is illustrated through an extensive simulation study and compared with other widely used anomaly detection methods. Real-data analyses involving wearable activity measurements and air pollution time series provide an assessment of its performance in real-world settings.
Comments35 pages, 12 figures
