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2019 Distributed statistical estimation and rates of convergence in normal approximation
Stanislav Minsker
Electron. J. Statist. 13(2): 5213-5252 (2019). DOI: 10.1214/19-EJS1647


This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important characteristic for large distributed systems. We establish connections between performance of these distributed algorithms and the rates of convergence in normal approximation, and prove non-asymptotic deviations guarantees, as well as limit theorems, for the resulting estimators. Our techniques are illustrated through several examples: in particular, we obtain new results for the median-of-means estimator, and provide performance guarantees for distributed maximum likelihood estimation.


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Stanislav Minsker. "Distributed statistical estimation and rates of convergence in normal approximation." Electron. J. Statist. 13 (2) 5213 - 5252, 2019.


Received: 1 February 2019; Published: 2019
First available in Project Euclid: 17 December 2019

zbMATH: 07147375
MathSciNet: MR4043072
Digital Object Identifier: 10.1214/19-EJS1647

Primary: 6F35
Secondary: 68W15

Keywords: Distributed estimation , median-of-means estimator , Normal approximation , robust estimation


Vol.13 • No. 2 • 2019
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