# Distributed Statistical Estimation and Rates of Convergence in Normal Approximation

## TL;DR

This paper introduces new distributed statistical estimation algorithms leveraging divide-and-conquer strategies, establishing their convergence rates and robustness, with applications to median-of-means and maximum likelihood estimators.

## Contribution

It develops novel algorithms for distributed estimation, linking their performance to normal approximation rates, and provides non-asymptotic deviation bounds and limit theorems.

## Key findings

- New bounds for median-of-means estimator in distributed settings
- Performance guarantees for distributed maximum likelihood estimation
- Robustness of divide-and-conquer algorithms in large systems

## Abstract

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.