We propose a new test to investigate the conditional mean dependence between a response variable and the corresponding covariates in the high-dimensional regimes. The test statistic is an extreme-type one built on the nonparametric method. The limiting null distribution of the proposed extreme type statistic under a mild mixing condition is established. Moreover, to make the test more powerful in general structures we propose a more general test statistic and develop its asymptotic properties. The power analysis of both methods is also considered. In real data analysis, we also propose a new way to conduct the feature screening based on our results. To evaluate the performance of our estimators and other methods, extensive simulations are conducted.

中文翻译：

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通过高维极端型统计量进行非参数条件均值检验

我们提出了一种新的检验来研究响应变量与高维体系中相应协变量之间的条件均值依赖性。检验统计量是一种建立在非参数方法基础上的极端型统计量。建立了温和混合条件下所提出的极端类型统计量的极限零分布。此外，为了使检验在一般结构中更加强大，我们提出了更一般的检验统计量并开发了其渐近性质。还考虑了两种方法的功效分析。在实际数据分析中，我们还提出了一种根据我们的结果进行特征筛选的新方法。为了评估我们的估计器和其他方法的性能，进行了广泛的模拟。