Year: 2024
Type: article
Abstract: 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.
Authors: Yeqing Zhou, Fei Jiang
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4403828337