We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on both US excess deaths data from 2017--2020 and S&P 500 data from the 2007--2008 financial crisis.

翻译：我们引入并研究与连续检测高维中值矢量变化相关的两个新的推论挑战。 首先,我们寻求对变化点的置信间隔, 其次,我们估算一组坐标指数,其中含有平均变化。 我们建议在线算法产生一个与平均检测延迟相同的间隔,其长度极有可能与平均检测延迟的顺序相同,达到对数系数。 相应的支持估算对假负数和假正数都有控制。 模拟证实了我们的方法的有效性,我们也说明了它对2017-2020年美国超额死亡数据和2007-2008年金融危机S&P500数据的适用性。