Heterogeneous Functional Regression for Subgroup Analysis
提出一种异质性函数回归方法，通过融合型分组惩罚同时进行参数估计和子组识别，适用于现代数据集中不同子样本间关系不同的场景，并在阿尔茨海默病数据上验证。
With ever increasing number of features of modern datasets, data heterogeneity is gradually becoming the norm rather than the exception. Whereas classical regressions usually assume all the samples follow a common model, it becomes imperative to identify the heterogeneous relationship in different subsamples. In this article, we propose a new approach to model heterogeneous functional regression relations. We target at the association between a response and a predictor, whose relationship can vary across underlying subgroups and is modeled as an unknown functional of an auxiliary predictor. We introduce a procedure which performs simultaneous parameter estimation and subgroup identification through a fusion type group-wise penalization. We establish the statistical guarantees in terms of non-asymptotic convergence of the parameter estimation. We also establish the oracle property and asymptotic normality of the estimators. We carry out intensive simulations, and illustrate with a new dataset from an Alzheimer's disease study. Supplementary materials for this article are available online.