Functional_Principa​l_Component_Analysi​s

This code is made based on Lirong SUN,et. al., "Interval-Valued Functional Principal omponent Analysis Method and Application Under the G".

Interval-valued functional principal component analysis (IFPCA) is a comprehensive eval-uation method that can effectively handle continuous high-frequency data. However, most existing IFPCA methods ssume that samples within intervals follow a uniform distribution, which may over-look the actual istribution of samples within intervals. This assumption may result in the omission of key features in amples, thereby affecting the accuracy of analyses. To address this issue, this study considers the internal distributional information of intervals using means and standard deviations to reflect the centralized ocation and discrete changes of intervals under the general distribution. The current time-varying distance function does not fully utilize this distributional information, necessitating an extension to accommodate the general distribution. Building on this, an IFPCA based on the time-varying distance function under the general distribution is proposed. This new IFPCA better utilizes the known internal information within intervals, uncovering intrinsic features of data. Simulation studies demonstrate the effectiveness of the FPCA under the general distribution. An empirical application further confirms that the new IFPCA is superior to existing IFPCA methods.