Composite quantile regression (CQR) is a robust and efficient estimation method. This paper studies CQR method for single-index models with ultra-high-dimensional data. We propose a penalized CQR estimator for single-index models and combine the debiasing technique with the CQR method to construct an estimator that is asymptotically normal, which enables the construction of valid confidence intervals and hypothesis testing. Both simulations and data analysis are conducted to illustrate the finite sample performance of the proposed methods.

中文翻译：

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超高维数据的单指标复合分位数回归

复合分位数回归 (CQR) 是一种稳健且有效的估计方法。本文研究了具有超高维数据的单指标模型的CQR方法。我们为单指数模型提出了一种惩罚 CQR 估计量，并将去偏技术与 CQR 方法相结合，以构建渐近正态的估计量，从而能够构建有效的置信区间和假设检验。进行了模拟和数据分析，以说明所提出方法的有限样本性能。