Functional principal component analysis (FPCA) is the most commonly used technique to analyze infinite‐dimensional functional data in finite lower‐dimensional space for the ease of computational intensity. However, the power of a test detecting the existence of a change‐point falls with the inclusion of more principal dimensions explaining a larger proportion of variability. We propose a new methodology for dynamically selecting the dimensions in FPCA that are used further for the testing of the existence of any change‐point in the given data. This data‐driven and efficient approach leads to a more powerful test than those available in the literature. We illustrate this method on the monthly global average anomaly of temperatures.

中文翻译：

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功能主成分分析中数据驱动的维度缩减，可识别功能数据中的变更点

功能主成分分析（FPCA）是在有限的低维空间中分析无限维功能数据以简化计算强度的最常用技术。但是，检测到变更点存在的测试的能力会下降，因为包含了更多的主要维度，可以解释更大范围的可变性。我们提出了一种动态选择FPCA中维的新方法，该维可进一步用于测试给定数据中是否存在任何变更点。与文献中可用的方法相比，这种由数据驱动的高效方法导致了更强大的测试。我们在全球每月平均温度异常上说明了这种方法。