Debiasing and Distributed Estimation for High-Dimensional Quantile Regression.

Area of Science:

• Statistics
• Computer Science
• Data Science

Background:

• The increasing volume of large datasets necessitates efficient computational methods.
• High-dimensional linear quantile regression presents unique statistical and computational challenges.
• Sparse coefficient assumption is common in high-dimensional models, often addressed with LASSO (Least Absolute Shrinkage and Selection Operator) regularization.

Purpose of the Study:

• To extend the debiasing procedure to quantile regression for sparse, high-dimensional data.
• To develop a divide-and-conquer distributed estimation approach suitable for big data.
• To address technical challenges including non-differentiable loss functions and conditional density estimation.

Main Methods:

• Extension of debiasing procedures from smooth parametric models to quantile regression.
• Application of LASSO penalty for sparse coefficient estimation.
• Development of a divide-and-conquer distributed estimation strategy.

Main Results:

• A novel debiased estimator for high-dimensional linear quantile regression is proposed.
• A distributed estimation framework is established, leveraging the debiased estimator.
• The method is shown to be effective for big data settings through numerical examples.

Conclusions:

• The proposed divide-and-conquer approach offers an effective solution for distributed estimation in high-dimensional linear quantile regression.
• The methodology successfully addresses challenges posed by large datasets and sparse coefficients.
• Numerical results validate the effectiveness of the distributed estimation strategy.