Distributed Subsampling and Quasi Decorrelated Score for Cluster Data: An Application to Beijing Multi-Site Air Quality

Forecasting and controlling PM2.5 emissions is crucial for environmental protection and public health. To analyze the Beijing multi-site air quality dataset on regional and seasonal effects in PM2.5 emissions, which has large-scale distributed cluster/longitudinal data and high-dimensional covariates, we develop a unified cluster subsampling method for generalized linear models (GLMs) to downsize the data volume and reduce computational burden. To incorporate the within-subject correlation, a weighted generalized estimation equations under an informative working correlation structure is considered and a novel optimal subsampling criterion including both the Aand L-optimality is proposed. For low-dimensional GLMs, the resulting optimal subsample estimators are consistent and asymptotically normal with explicitly derived asymptotic covariance matrices. For the preconceived lowdimensional parameter in high-dimensional GLMs, a quasi decorrelated score function is developed to mitigate the effect from nuisance parameter estimation. Our proposed method is evaluated by simulation. By applying our method to the Beijing multi-site air quality dataset, we reveal that the PM2.5 emissions in the south part of Beijing have a U-shaped seasonal effect in the order of winter, spring, summer, and autumn, and a regional aggregation effect in winter of the southeastern of Beijing. © 2025 Institute of Mathematical Statistics