Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control
Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control
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DOI：
10.1093/biomet/asr016
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发表时间：
2011-06-01
期刊：
影响因子：
2.7
通讯作者：
Finos, Livio
中科院分区：
文献类型：
--
作者：
Goeman, Jelle J.;Van Houwelingen, Hans C.;Finos, Livio
针对广义线性模型中的高维备选方案测试低维零假设可能导致检验统计量，该检验统计量是零模型下的残差中的二次型。利用渐近变元，我们证明了这种检验统计量的分布可以用正态变量的二次型之比来近似，这一点的算法很容易得到。对于广义线性模型，即使当模型中协变量的个数远远超过样本量时，渐近分布对中、小样本的I型误差也有很好的控制效果。
Testing a low-dimensional null hypothesis against a high-dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model. Using asymptotic arguments, we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables, for which algorithms are readily available. For generalized linear models, the asymptotic distribution shows good control of type I error for moderate to small samples, even when the number of covariates in the model far exceeds the sample size.