Testing Regression Coefficients in High-Dimensional and Sparse Settings
Testing Regression Coefficients in High-Dimensional and Sparse Settings
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DOI：
10.1007/s10114-021-9468-8
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Kai Xu;Yan Tian;Q. Cheng
中科院分区：
文献类型：
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作者：
Kai Xu;Yan Tian;Q. Cheng
在高维环境下，本文考虑了多元分析中的一个典型检验问题，即线性回归模型中的系数检验问题。在最近的文献中已经提出了几种高维回归系数的检验方法。然而，这些检验是基于平方类型统计量的和，这些统计量在密集备选方案下表现良好，而在稀疏备选方案下表现得很差。为了解决这一问题，我们引入了一种新的检验统计量，该统计量基于最大型统计量，放大了稀疏信号。证明了检验统计量的极限零分布为第I类极值分布，并分析了检验的威力。特别地，从理论上和数值上证明了该检验对稀疏方案是有效的。进行了数值研究，以检验该测试的数值性能，并将其与文献中提供的其他测试进行比较。
In the high-dimensional setting, this article considers a canonical testing problem in multivariate analysis, namely testing coefficients in linear regression models. Several tests for high-dimensional regression coefficients have been proposed in the recent literature. However, these tests are based on the sum of squares type statistics, that perform well under the dense alternatives and suffer from low power under the sparse alternatives. In order to attack this issue, we introduce a new test statistic which is based on the maximum type statistic and magnifies the sparse signals. The limiting null distribution of the test statistic is shown to be the extreme value distribution of type I and the power of the test is analysed. In particular, it is shown theoretically and numerically that the test is powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature.