# Distributed Statistical Estimation and Rates of Convergence in Normal Approximation

arXiv: https://arxiv.org/abs/1704.02658 · HTML: https://mlsanity.com/paper/1704.02658/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2017.

## Built on by (most cited first, 15 of 15)

- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference](https://mlsanity.com/paper/2103.02860/) (2021)
- [Bandits Corrupted by Nature: Lower Bounds on Regret and Robust Optimistic Algorithm](https://mlsanity.com/paper/2203.03186/) (2022)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [Optimality in Mean Estimation: Beyond Worst-Case, Beyond Sub-Gaussian, and Beyond 1+α Moments](https://mlsanity.com/paper/2311.12784/) (2023)
- [Distributed Sparse Normal Means Estimation with Sublinear Communication](https://mlsanity.com/paper/2102.03060/) (2021)
- [Robust Score Matching](https://mlsanity.com/paper/2501.05105/) (2025)
- [Collaborative Learning of Discrete Distributions under Heterogeneity and Communication Constraints](https://mlsanity.com/paper/2206.00707/) (2022)
- [Byzantine-tolerant distributed learning of finite mixture models](https://mlsanity.com/paper/2407.13980/) (2024)
- [Divide-and-conquer methods for big data analysis](https://mlsanity.com/paper/2102.10771/) (2021)
- [Classical Shadows with Improved Median-of-Means Estimation](https://mlsanity.com/paper/2412.03381/) (2024)
- [Learning Centre Partitions from Summaries](https://mlsanity.com/paper/2509.16337/) (2025)
- [On the Optimality of the Median-of-Means Estimator under Adversarial Contamination](https://mlsanity.com/paper/2510.07867/) (2025)
- [Robust Variational Bayes by Min-Max Median Aggregation](https://mlsanity.com/paper/2512.12676/) (2025)
- [HOMER: Huber-of-Means for Efficient and Robust Estimation in Hilbert Spaces](https://mlsanity.com/paper/2607.27532/) (2026)

## Abstract (arXiv)

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, as well as provide performance guarantees for distributed maximum likelihood estimation.