Testing covariates in high-dimensional regression
Testing covariates in high-dimensional regression
复制标题
测试高维回归中的协变量
DOI：
10.1007/s10463-013-0414-0
复制
发表时间：
2014-04-01
影响因子：
1
通讯作者：
Tsai, Chih-Ling
中科院分区：
文献类型：
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作者：
Lan, Wei;Wang, Hansheng;Tsai, Chih-Ling
在高维线性回归模型中，我们提出了一个新的方法来检验回归系数子集的统计显著性。具体而言，我们采用响应变量和检验协变量之间的偏协方差来获得检验统计量。即使预测维度远大于样本量，所得检验也适用。在原假设下，结合预测量的有界性和矩条件，我们证明了所提出的检验统计量是渐近标准正态的，并得到了Monte Carlo实验的进一步支持.类似的检验可以扩展到广义线性模型。通过付费搜索广告的实证示例说明了该测试的实际有用性。
In a high-dimensional linear regression model, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting test is applicable even if the predictor dimension is much larger than the sample size. Under the null hypothesis, together with boundedness and moment conditions on the predictors, we show that the proposed test statistic is asymptotically standard normal, which is further supported by Monte Carlo experiments. A similar test can be extended to generalized linear models. The practical usefulness of the test is illustrated via an empirical example on paid search advertising.