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AN ITERATIVE REWEIGHTED ALGORITHM FOR HIGH DIMENSIONAL SPARSE QUANTILE REGRESSION WITH ERROR FUNCTION REGULARIZATION
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DOI：10.3934/jimo.2025138.png)
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Abstract
En 中文
. High-dimensional quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection. However, many existing penalized quantile regression often leads to significant estimation bias, and employing non-convex penalties can reduce bias but significantly increases computational complexity. To address these challenges, we propose an iterative reweighted algorithm for high-dimensional sparse quantile regression (HDSQR). First, we introduce a convolution-smoothed technique for HDSQR based on the error function regularization, namely HDSQR-EFR, which demonstrates robustness and reduced estimation bias compared to the existing regularization while maintaining computational efficiency. Second, we develop an integrated framework that combines the iterative reweighted & ell;1 algorithm with a gradientbased local adaptive majorize-minimization algorithm to efficiently solve the proposed HDSQR-EFR model. Third, comprehensive numerical studies show that our method consistently outperforms existing HDSQR techniques by providing accurate parameter estimation and effective variable selection. Finally, we validate our method using riboflavin gene expression data, highlighting its applicability to real-world, high-dimensional settings.
Keywords:
Key wordsQuantile regression
sparse optimization
iterative reweighted algorithm
error function regularization
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