A Sequential Nonparametric Test for Detecting Change in the Distribution Based on Energy Statistics

Abstract In this article, we propose a sequential nonparametric test based on windowed energy statistics (Sźekely and Rizzo 2013) to detect changes in the distribution of independent random variables. The proposed method is simple and does not rely on the choice of kernel such as U-statistic-based tests to detect any distributional changes regardless of type. In addition, the method does not require the parametric assumptions for both the null and alternative distributions. We illustrate that the proposed method outperforms other existing methods in the sequential testing procedure in terms of the false-alarm rate and power through simulations. We then apply the method to the problem of detecting radiological anomalies using datasets provided by Padila et al. (2019) for the background gamma-radiation spectrum on a large university campus. We observe success in improving the time-to-detection for any type of radiological anomalies.