Robust estimation for nonrandomly distributed data

Shaomin Li (), Kangning Wang () and Yong Xu ()
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Shaomin Li: Beijing Normal University
Kangning Wang: Shandong Technology and Business University
Yong Xu: Shandong Technology and Business University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 3, No 4, 493-509

Abstract: Abstract In recent years, many methodologies for distributed data have been developed. However, there are two problems. First, most of these methods require the data to be randomly and uniformly distributed across different machines. Second, the methods are mainly not robust. To solve these problems, we propose a distributed pilot modal regression estimator, which achieves robustness and can adapt when the data are stored nonrandomly. First, we collect a random pilot sample from different machines; then, we approximate the global MR objective function by a communication-efficient surrogate that can be efficiently evaluated by the pilot sample and the local gradients. The final estimator is obtained by minimizing the surrogate function in the master machine, while the other machines only need to calculate their gradients. Theoretical results show the new estimator is asymptotically efficient as the global MR estimator. Simulation studies illustrate the utility of the proposed approach.

Keywords: Distributed data; Communication-efficient; Modal regression; Robustness (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00852-4

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