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

Abstract

Data availability: The air-quality data from the Beijing Municipal Environmental Monitoring Center is available from online site: https://archive.ics.uci.edu/dataset/501/beijing+multi+site+air+quality+data .Supplementary material: Supplementary data are available online at: https://academic.oup.com/jrsssc/advance-article/doi/10.1093/jrsssc/qlag005/8489473#supplementary-data .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.This research was supported by the Research Project of Humanities and Social Sciences, Ministry of Education of China (Grant No. 25YJA910003); the National Social Science Fund of China (Grant No. 25BTJ041); the National Key R&D Program of China (Grant No. 2024YFA1013502); the National Natural Science Foundation of China (Grant Nos. U23A2064, 12531013); the Natural Science Foundation of Zhejiang Province (Grant No. LY24A010004); and the Chern Institute of Mathematics Visiting Scholar Program