Zhou Yeqing, Jiang Fei
School of Mathematical Sciences, School of Economics and Management, and Key Laboratory of Intelligent Computing and Applications, Tongji University, Shanghai, China.
Department of Epidemiology and Biostatistics, The University of California, San Francisco, San Francisco, CA.
J Comput Graph Stat. 2024 Dec 20. doi: 10.1080/10618600.2024.2414113.
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.
随着现代数据集的特征数量不断增加，数据异质性正逐渐成为常态而非例外。经典回归通常假设所有样本都遵循一个共同模型，因此识别不同子样本中的异质关系变得势在必行。在本文中，我们提出了一种新方法来对异质函数回归关系进行建模。我们针对响应变量和预测变量之间的关联，其关系可能在不同的潜在子组中有所不同，并被建模为辅助预测变量的未知函数。我们引入了一种通过融合型组内惩罚进行同时参数估计和子组识别的方法。我们在参数估计的非渐近收敛方面建立了统计保证。我们还建立了估计量的神谕性质和渐近正态性。我们进行了大量模拟，并以一项阿尔茨海默病研究的新数据集进行了说明。本文的补充材料可在线获取。
