Analysis of tail quantiles of the response distribution is sometimes more important than the mean in biomarker studies. Inference in quantile regression is complicated when there exist a large number of candidate markers together with some pre-specified controlled covariates. In this paper, we develop a new and simple testing procedure to detect the effects of biomarkers in high-dimensional quantile regression in the presence of protected covariates. The test is based on the maximum-score-type statistic obtained from conditional marginal regression. We establish the asymptotic properties of the proposed test statistic under both null and alternative hypotheses, and further propose an alternative multiplier bootstrap method with theoretical justifications. We demonstrate through numerical studies that the proposed method provides adequate controls of the family-wise error rate with competitive power, and it can also be used as a stopping rule in the forward regression. The proposed method is applied to a motivating genome-wide association study Corresponding author, email: dairy-2006@163.com. Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)

中文翻译：

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高维分位数回归的条件边际检验

在生物标志物研究中，响应分布的尾部分位数分析有时比平均值更重要。当存在大量候选标记和一些预先指定的受控协变量时，分位数回归中的推理很复杂。在本文中，我们开发了一种新的简单测试程序，以检测生物标志物在存在受保护协变量的情况下在高维分位数回归中的影响。该检验基于从条件边际回归中获得的最大分数型统计量。我们在原假设和替代假设下建立了所提出的检验统计量的渐近特性，并进一步提出了一种具有理论依据的替代乘数自举方法。我们通过数值研究证明，所提出的方法对具有竞争力的家庭错误率提供了足够的控制，并且它还可以用作前向回归中的停止规则。所提出的方法应用于激励全基因组关联研究通讯作者，电子邮件：乳品-2006@163.com。Statistica Sinica：新接受的论文（接受的作者版本需英文编辑）