Sufficient variable screening (SVS) with the false discovery rate (FDR) controlled rapidly reduces dimensionality with high probability in high dimensional modeling. By using quantiles, this paper proposes a new SVS procedure by controlling the FDR based on two‐stage Pearson's goodness testing with Chi‐square statistics for high dimensional data, abbreviated as QC‐SVS‐FDR. Without any specified distribution of the actual model, the QC‐SVS‐FDR method screens important predictors by a series of testing procedures combined with the adaptive composite of Pearson's chi‐square statistics. The quantile correlation‐based sufficient utility is sensitive to capture the subtle correlations under different quantile levels and is easy to implement with computational efficiency. Asymptotic results and sufficient screening properties of the proposed methods are obtained under mild conditions. Numerical studies including simulation studies and real data analysis demonstrate the advantages of the proposed method in practical settings.

中文翻译：

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通过控制错误发现率进行基于分位数相关性的充分变量筛选

在高维建模中，充分变量筛选（SVS）和错误发现率（FDR）控制能够以高概率快速降低维度。本文利用分位数，提出了一种基于高维数据卡方统计两阶段 Pearson 优度检验控制 FDR 的 SVS 程序，简称 QC-SVS-FDR。在没有实际模型的任何指定分布的情况下，QC-SVS-FDR 方法通过一系列测试程序结合 Pearson 卡方统计的自适应组合来筛选重要的预测变量。基于分位数相关性的充分效用对于捕获不同分位数水平下的微妙相关性很敏感，并且易于实现且计算效率高。所提出的方法在温和的条件下获得了渐近结果和足够的筛选特性。包括模拟研究和真实数据分析在内的数值研究证明了该方法在实际环境中的优势。