We consider change-point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. We propose a nonparametric approach using a single index model (SIM), where instead of monitoring the profile itself for a change, we monitor an $l_2$-based statistic on the coefficients generated by the SIM. Through simulation we show our novel method outperforms existing multivariate profile monitoring methods.

中文翻译：

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使用单指标模型进行非线性剖面监测

我们考虑功能观察序列中的变化点检测和估计。当过程的质量以此类观察为特征时，通常会出现此设置，称为配置文件，并且可以使用监控结构变化的配置文件来确保过程随时间推移的稳定性。我们提出了一种使用单索引模型 (SIM) 的非参数方法，在这种方法中，我们不是监控配置文件本身的变化，而是监控一个${升}_2$-基于由 SIM 生成的系数的统计量。通过模拟，我们展示了我们的新方法优于现有的多变量剖面监测方法。