论文标题
对高维数据的无模型统计推断
Model-Free Statistical Inference on High-Dimensional Data
论文作者
论文摘要
本文旨在为高维数据开发有效的无模型推理程序。我们首先通过足够的降低框架重新重新制定了假设检验问题。借助新的重新重新制定，我们提出了一个新的测试统计数据，并表明其渐近分布为$χ^2 $分布，其自由度不取决于未知的人口分布。我们在当地替代假设下进一步进行功率分析。此外，我们研究了如何控制相关的$χ^2 $测试的错误发现率，以识别无模型框架下的重要预测因子。为此，我们提出了一个多重测试程序，并建立了其理论保证。进行了蒙特卡洛模拟研究以评估所提出的测试的性能，对现实世界数据集的经验分析用于说明所提出的方法。
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is $χ^2$ distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed $χ^2$ tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world data set is used to illustrate the proposed methodology.
