α-separability and adjustable combination of amplitude and phase model for functional data
提出α可分离性概念，通过构建α索引度量族来分离并联合建模函数型数据的振幅和相位变化，参数α允许用户自定义对垂直和水平特征的建模侧重，并在COVID-19感染率数据上验证。
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.