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Distributed Estimation for ℓ 0 -Constrained Quantile Regression Using Iterative Hard Thresholding

Author

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  • Zhihe Zhao

    (Department of Mathematics, City University of Hong Kong, Hong Kong, China)

  • Heng Lian

    (Department of Mathematics, City University of Hong Kong, Hong Kong, China)

Abstract

Distributed frameworks for statistical estimation and inference have become a critical toolkit for analyzing massive data efficiently. In this paper, we present distributed estimation for high-dimensional quantile regression with ℓ 0 constraint using iterative hard thresholding (IHT). We propose a communication-efficient distributed estimator which is linearly convergent to the true parameter up to the statistical precision of the model, despite the fact that the check loss minimization problem with an ℓ 0 constraint is neither strongly smooth nor convex. The distributed estimator we develop can achieve the same convergence rate as the estimator based on the whole data set under suitable assumptions. In our simulations, we illustrate the convergence of the estimators under different settings and also demonstrate the accuracy of nonzero parameter identification.

Suggested Citation

  • Zhihe Zhao & Heng Lian, 2025. "Distributed Estimation for ℓ 0 -Constrained Quantile Regression Using Iterative Hard Thresholding," Mathematics, MDPI, vol. 13(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:669-:d:1594032
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    References listed on IDEAS

    as
    1. Huixia Judy Wang & Deyuan Li, 2013. "Estimation of Extreme Conditional Quantiles Through Power Transformation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1062-1074, September.
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