# Distributed inference for quantile regression processes

arXiv: https://arxiv.org/abs/1701.06088 · HTML: https://mlsanity.com/paper/1701.06088/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2017.

## Built on by (most cited first, 11 of 11)

- [Distributed Bootstrap for Simultaneous Inference Under High Dimensionality](https://mlsanity.com/paper/2102.10080/) (2021)
- [Fast and Robust Sparsity Learning over Networks: A Decentralized Surrogate Median Regression Approach](https://mlsanity.com/paper/2202.05498/) (2022)
- [Adaptive Data Fusion for Multi-task Non-smooth Optimization](https://mlsanity.com/paper/2210.12334/) (2022)
- [Distributed Semi-Supervised Sparse Statistical Inference](https://mlsanity.com/paper/2306.10395/) (2023)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [MANDERA: Malicious Node Detection in Federated Learning via Ranking](https://mlsanity.com/paper/2110.11736/) (2021)
- [Distributed Estimation and Inference for Semi-parametric Binary Response Models](https://mlsanity.com/paper/2210.08393/) (2022)
- [Distributed Linear Regression with Compositional Covariates](https://mlsanity.com/paper/2310.13969/) (2023)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)
- [Central Limit Theorems for Stochastic Gradient Descent Quantile Estimators](https://mlsanity.com/paper/2503.02178/) (2025)
- [Distributional Off-Policy Evaluation with Deep Quantile Process Regression](https://mlsanity.com/paper/2604.18143/) (2026)

## Abstract (arXiv)

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated quantile curves. Our general quantile regression framework covers both linear models with fixed or growing dimension and series approximation models. We prove that the proposed procedure does not sacrifice any statistical inferential accuracy provided that the number of distributed computing units and quantile levels are chosen properly. In particular, a sharp upper bound for the former and a sharp lower bound for the latter are derived to capture the minimal computational cost from a statistical perspective. As an important application, the statistical inference on conditional distribution functions is considered. Moreover, we propose computationally efficient approaches to conducting inference in the distributed estimation setting described above. Those approaches directly utilize the availability of estimators from sub-samples and can be carried out at almost no additional computational cost. Simulations confirm our statistical inferential theory.