Communication-efficient estimation and inference for high-dimensional quantile regression based on smoothed...

Area of Science:

• Statistical Learning
• High-Dimensional Data Analysis
• Distributed Systems

Background:

• Distributed estimation is crucial in modern statistical learning, but faces challenges with small local sample sizes and high-dimensional covariates.
• Existing methods struggle with slow convergence rates for nuisance parameter estimation in such distributed settings.

Purpose of the Study:

• To develop communication-efficient distributed estimators for a low-dimensional parameter vector in high-dimensional quantile regression.
• To address the challenges posed by small local sample sizes and large covariate dimensions in distributed data settings.

Main Methods:

• Generalizing the decorrelated score approach to improve nuisance parameter estimation.
• Employing smoothing techniques within multiround algorithms for enhanced efficiency.
• Proposing two novel communication-efficient distributed estimators.

Main Results:

• Theoretical risk bounds and limiting distributions for the proposed estimators are derived.
• The estimators demonstrate effective performance in finite sample simulations.
• The methods are validated through an application to a gene expression dataset.

Conclusions:

• The proposed distributed estimation methods effectively handle high-dimensional quantile regression with small local sample sizes.
• These techniques offer improved accuracy and efficiency for distributed statistical learning.
• The study provides practical tools for analyzing complex, distributed datasets.