Robust distributed estimation and variable selection for massive datasets via rank regression

Jiaming Luan, Hongwei Wang, Kangning Wang () and Benle Zhang
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Jiaming Luan: Shandong Technology and Business University
Hongwei Wang: Shandong Technology and Business University
Kangning Wang: Shandong Technology and Business University
Benle Zhang: Shandong Technology and Business University

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 3, No 2, 435-450

Abstract: Abstract Rank regression is a robust modeling tool; it is challenging to implement it for the distributed massive data owing to memory constraints. In practice, the massive data may be distributed heterogeneously from machine to machine; how to incorporate the heterogeneity is also an interesting issue. This paper proposes a distributed rank regression ( $$\mathrm {DR}^{2}$$ DR 2 ), which can be implemented in the master machine by solving a weighted least-squares and adaptive when the data are heterogeneous. Theoretically, we prove that the resulting estimator is statistically as efficient as the global rank regression estimator. Furthermore, based on the adaptive LASSO and a newly defined distributed BIC-type tuning parameter selector, we propose a distributed regularized rank regression ( $$\mathrm {DR}^{3}$$ DR 3 ), which can make consistent variable selection and can also be easily implemented by using the LARS algorithm on the master machine. Simulation results and real data analysis are included to validate our method.

Keywords: Massive data; Robustness; Communication efficient; Variable selection (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10463-021-00803-5

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