Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean‐shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence structures and mild moment conditions. Specifically, we show that with a boundary removal parameter the bootstrap CUSUM test enjoys the uniform validity in size under the null and it achieves the minimax separation rate under the sparse alternatives when the dimension p can be larger than the sample size n.

中文翻译：

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高维均值向量的有限样本变化点推断和识别

累积总和（CUSUM）统计信息广泛用于变更点推断和识别。对于测试均值漂移模型生成的独立样本中是否存在变化点的问题，我们引入了高斯乘数自举法，以在高维度上校准CUSUM测试统计数据的关键值。提出的自举CUSUM测试完全依赖数据，并且在任意依赖结构和轻度弯矩条件下都具有很强的理论保证。具体而言，我们表明，使用边界消除参数，自举CUSUM检验在零值条件下在大小上享有统一的有效性，并且在维数p可以大于样本大小n时，在稀疏替代项下可以实现最小最大分离率。