Deep Regression for Repeated Measurements

• 成果类型: Article; Early Access
• 署名作者: Yan, Shunxing; Yao, Fang; Zhou, Hang
• 署名单位: Peking University; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2458344
• 发表日期: 2025
• 关键词: local linear-regression; network approximation; neural-networks; models; dimensionality; CONVERGENCE; MANIFOLDS; SPARSE; bounds

摘要

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected deep neural network (DNN) estimators with flexible shapes. A novel theoretical framework allowing arbitrary sampling frequency is established by adopting empirical process techniques to tackle clustered dependence. We then consider the DNN estimators for Holder target function and illustrate a key phenomenon, the phase transition in the convergence rate, inherent to repeated measurements and its connection to the curse of dimensionality. Furthermore, we study several examples with low intrinsic dimensions, including the hierarchical composition model, low-dimensional support set and anisotropic Holder smoothness. We also obtain new approximation results and matching lower bounds to demonstrate the adaptivity of the DNN estimators for circumventing the curse of dimensionality. Simulations and real data examples are provided to support our theoretical findings and practical implications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.