In this article, we propose a new technique for constructing confidence intervals for the mean of a noisy sequence with multiple change‐points. We use the weighted bootstrap to generalize the bootstrap aggregating or bagging estimator. A standard deviation formula for the bagging estimator is introduced, based on which smoothed confidence intervals are constructed. To further improve the performance of the smoothed interval for weak signals, we suggest a strategy of adaptively choosing between the percentile intervals and the smoothed intervals. A new intensity plot is proposed to visualize the pattern of the change‐points. We also propose a new change‐point estimator based on the intensity plot, which has superior performance in comparison with the state‐of‐the‐art segmentation methods. The finite sample performance of the confidence intervals and the change‐point estimator are evaluated through Monte Carlo studies and illustrated with a real data example.

中文翻译：

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多个变更点模型的统计推断

在本文中，我们提出了一种新技术，用于构造具有多个变化点的嘈杂序列均值的置信区间。我们使用加权的引导程序来概括引导程序的聚集或装袋估计量。介绍了用于装袋估算器的标准偏差公式，在此基础上构造了平滑的置信区间。为了进一步改善弱信号的平滑间隔的性能，我们建议一种在百分比间隔和平滑间隔之间自适应选择的策略。提出了一个新的强度图，以可视化变化点的模式。我们还基于强度图提出了一种新的变化点估计器，与最新的分割方法相比，它具有更好的性能。