α-separability and adjustable combination of amplitude and phase model for functional data
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2025 · Volume 87 · Issue 3
Abstract
We consider separating and joint modelling amplitude and phase variations for functional data in an identifiable manner. To rigorously address this separability issue, we introduce the notion of α-separability upon constructing a family of α -indexed metrics. We bridge α -separability with the uniqueness of Fréchet mean, leading to the proposed adjustable combination of amplitude and phase model. The parameter α allows user-defined modelling emphasis between vertical and horizontal features and provides a novel viewpoint on the identifiability issue. We prove the consistency of the sample Fréchet mean and variance, and the proposed estimators. Our method is illustrated in simulations and COVID-19 infection rate data.
Keywords
Fréchet mean, functional data analysis, identifiability, joint model, separability, variation decomposition
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