Data-driven dimension reduction in functional principal component analysis identifying the change-point in functional data

Abstract

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.