Functional regression with intensively measured longitudinal outcomes: a new lens through data partitioning

Abstract Modern longitudinal data from wearable devices consist of biological signals at high‐frequency time points. Distributed statistical methods have emerged as a powerful tool to overcome the computational burden of estimation and inference with large data, but methodology for distributed functional regression remains limited. We propose a distributed estimation and inference procedure that efficiently estimates both functional and scalar parameters with intensively measured longitudinal outcomes. The procedure overcomes computational difficulties through a scalable divide‐and‐conquer algorithm that partitions the outcomes into smaller sets. We circumvent traditional basis selection problems by analyzing data using quadratic inference functions in smaller subsets such that the basis functions have a low dimension. To address the challenges of combining estimates from dependent subsets, we propose a statistically efficient one‐step estimator derived from a constrained generalized method of moments objective function with a smoothing penalty. We show theoretically and numerically that the proposed estimator is as statistically efficient as non‐distributed alternative approaches and more efficient computationally. We demonstrate the practicality of our approach with the analysis of accelerometer data from the National Health and Nutrition Examination Survey.