Deep Regression for Repeated Measurements

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 Hölder 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 Hölder 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.

搜集汇总

背景与挑战

背景概述

该数据集研究了使用深度神经网络进行非参数均值函数回归的方法，特别关注重复测量数据的处理，并提供了理论框架、模拟和实际数据示例以支持研究发现。