AI 中文总结
该研究针对高维数据序列均值的多变化点检测问题，采用自下而上的方法，计算相邻段的\(L_2\)和\(L_\infty\)聚合检验统计量并结合秩信息，能自适应处理不同稀疏性，证明了其在多种噪声下的一致性，通过模拟和实例展示了实用性。
AI 中文摘要
我们介绍了一种用于检测高维数据序列均值中多个变化点的方法。与现有的自上而下（即分裂）算法不同，我们采用自下而上（即凝聚）的方法，从最精细级别开始迭代合并相邻数据段。对于具有频繁变化点的信号尤为有用，因为在将段合并为更粗的摘要之前会评估局部证据。我们计算相邻段的\(L_2\)和\(L_\infty\)聚合检验统计量，并结合各自秩的信息，使该方法能自适应处理不同程度的变化点稀疏性。我们证明了在独立同分布高斯噪声以及可能相关和/或非高斯噪声下，估计的变化点数量和位置的一致性。通过模拟和涉及英国房价指数数据的实际例子证明了我们方法的实用性。
英文摘要
We introduce a method for detecting multiple change-points in the mean of a high-dimensional data sequence. Unlike existing top-down (i.e. divisive) algorithms, we adopt a bottom-up (i.e. agglomerative) approach, whereby we iteratively merge neighboring segments of data starting from the finest level. This is particularly useful for signals with frequent change-points, since local evidence is assessed before segments are combined into coarser summaries. We compute $L_2$- and $L_\infty$-aggregated test statistics of neighboring segments and combine the information from their respective ranks, which makes the method adaptive in handling different degrees of change-point sparsity. We show the consistency of the estimated number and locations of change-points under both iid Gaussian and possibly dependent and/or non-Gaussian noise. The practicality of our approach is demonstrated through simulations and a real data example involving the UK House Price Index data.
Comments36 pages, 4 figues
