Abstract

In a high-dimensional linear regression model, this article is concerned with testing statistical significance of a subset of regression coefficients. The conventional partial F-test is not applicable in high-dimensional situations. Several methods for testing whether any of the discarded covariates is significant conditional on relative importance of predictors have been proposed in the recent literature, but they are adversely affected by the overestimation of the variance. To overcome this issue, we propose a novel nonparametric testing procedure to avoid this problem and enhance the empirical power. In addition, the new test is very effective when error distribution deviates from the normal scenario and can integrate all the individual information of the discarded covariates. Under the high-dimensional null and alternative hypotheses, we derive the asymptotic distribution of the proposed test statistic, which allows power evaluation of the test. Numerical studies are carried out to examine the numerical performance of the test. The results show that the test proposed here behaves well in terms of sizes and power and significantly outperforms the existing choices in a range of settings.

摘要

在高维线性回归模型中，本文关注的是检验回归系数子集的统计显着性。常规偏F-test 不适用于高维情况。在最近的文献中已经提出了几种方法来测试任何丢弃的协变量是否显着取决于预测变量的相对重要性，但它们受到方差高估的不利影响。为了克服这个问题，我们提出了一种新的非参数测试程序来避免这个问题并增强经验能力。此外，新测试在误差分布偏离正常情况时非常有效，并且可以整合丢弃协变量的所有个体信息。在高维零假设和替代假设下，我们推导了所提出的检验统计量的渐近分布，从而可以对检验进行功效评估。进行数值研究以检查测试的数值性能。结果表明，此处提出的测试在大小和功率方面表现良好，并且在一系列设置中明显优于现有选择。