Simulation study demonstrates distributed estimation reduces computation time while maintaining accuracy in functional regression models, indicating scalable analysis without raw data sharing.
This paper proposes distributed estimation procedures for three scalar-on-function regression models: the functional linear model (FLM), the functional non-parametric model (FNPM), and the functional partial linear model (FPLM). The framework addresses two key challenges in functional data analysis: the high computational cost of large samples and the limitations on sharing raw data across institutions. Monte Carlo simulations show that the distributed estimators substantially reduce computation time while preserving high estimation and prediction accuracy for all three models. When block sizes become too small, the FPLM exhibits overfitting, leading to narrower prediction intervals and reduced empirical coverage probability. Two empirical studies based on the tecator and air quality data further support these findings.
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He et al. (2026) studied this question.
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