2024/05/23 by Guanghui Cheng, Wenjuan Hu, Cheng, Guanghui +5
Engineering · Mathematics · #Advanced Control Systems Optimization #Computation (stat.CO) #FOS: Computer and information sciences #Fault Detection and Control Systems #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2405.14628
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel and robust online function-on-scalar regression technique via geometric median to learn associations between functional responses and scalar covariates based on massive or streaming datasets. The online estimation procedure, developed using the average stochastic gradient descent algorithm, offers an efficient and cost-effective method for analyzing sequentially augmented datasets, eliminating the need to store large volumes of data in memory. We establish the almost sure consistency, Lp convergence, and asymptotic normality of the online estimator. To enable efficient and fast inference of the parameters of interest, including the derivation of confidence intervals, we also develop an innovative two-step online bootstrap procedure to approximate the limiting error distribution of the robust online estimator. Numerical studies under a variety of scenarios demonstrate the effectiveness and efficiency of the proposed online learning method. A real application analyzing PM2.5 air-quality data is also included to exemplify the proposed online approach.