A communication-efficient distributed Retire with application to the analysis of multi-site air-quality distributed data

Abstract A multi-site city air-quality dataset should be considered distributed data as it is generated from multiple geographically dispersed sources, such as air quality sensors or monitoring stations. In various fields, distributed systems are increasingly employed to handle data collected from diverse sources, often resulting in datasets that are heavy-tailed, asymmetric, or heterogeneous. Robust expectile regression combines the computational efficiency of expectile regression with its robustness in handling heavy-tailed response distributions and outliers. This paper extends robust expectile regression to communication-efficient distributed systems and applies it to the analysis of multi-site air-quality datasets. The proposed distributed estimators achieve both computational and communication efficiency while delivering statistical performance comparable to global estimators, as demonstrated through both theoretical analysis and numerical experiments.