&NA; Multivariate regression with high‐dimensional covariates has many applications in genomic and genetic research, in which some covariates are expected to be associated with multiple responses. This paper considers joint testing for regression coefficients over multiple responses and develops simultaneous testing methods with false discovery rate control. The test statistic is based on inverse regression and bias‐corrected group lasso estimates of the regression coefficients and is shown to have an asymptotic chi‐squared null distribution. A row‐wise multiple testing procedure is developed to identify the covariates associated with the responses. The procedure is shown to control the false discovery proportion and false discovery rate at a prespecified level asymptotically. Simulations demonstrate the gain in power, relative to entrywise testing, in detecting the covariates associated with the responses. The test is applied to an ovarian cancer dataset to identify the microRNA regulators that regulate protein expression.

中文翻译：

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高维多元回归中的联合测试和错误发现率控制

&NA; 具有高维协变量的多元回归在基因组和遗传研究中有许多应用，其中一些协变量预计与多重响应相关。本文考虑对多个响应的回归系数进行联合测试，并开发具有错误发现率控制的同步测试方法。检验统计量基于回归系数的逆回归和偏差校正组套索估计，并显示具有渐近卡方零分布。开发了逐行多重测试程序来识别与响应相关的协变量。该过程被证明是渐近地将错误发现比例和错误发现率控制在预先指定的水平。模拟证明了功率的增加，相对于入门测试，检测与响应相关的协变量。该测试应用于卵巢癌数据集，以确定调节蛋白质表达的 microRNA 调节因子。