High-dimensional general linear hypothesis tests via non-linear spectral shrinkage
High-dimensional general linear hypothesis tests via non-linear spectral shrinkage
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DOI：
10.3150/19-bej1186
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发表时间：
2018-10
期刊：
影响因子：
1.5
通讯作者：
Haoran Li;Alexander Aue;D. Paul
中科院分区：
文献类型：
--
作者：
Haoran Li;Alexander Aue;D. Paul
我们感兴趣的是在高维多元线性回归模型中检验一般线性假设。该框架包括许多深入研究的问题，如两个样本检验的平等的人口手段，MANOVA和其他特殊情况。一个家庭的旋转不变的测试，提出了一个灵活的频谱收缩计划适用于样本误差协方差矩阵。假设观测值存在某些矩，在维度与样本量相当的情况下，推导出零假设下检验统计量的渐近正态性。在各种局部替代方案下研究了所提出的检验的渐进功效。功率特性，然后利用提出一个数据驱动的选择的频谱收缩函数。作为一般理论的一个例子，我们构建了一个家庭的测试涉及脊型正则化，并建议可能的扩展到更复杂的正则化。进行了模拟研究，以检查所提出的测试的数值性能。
We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and others as special cases. A family of rotation-invariant tests is proposed that involves a flexible spectral shrinkage scheme applied to the sample error covariance matrix. The asymptotic normality of the test statistic under the null hypothesis is derived in the setting where dimensionality is comparable to sample sizes, assuming the existence of certain moments for the observations. The asymptotic power of the proposed test is studied under various local alternatives. The power characteristics are then utilized to propose a data-driven selection of the spectral shrinkage function. As an illustration of the general theory, we construct a family of tests involving ridge-type regularization and suggest possible extensions to more complex regularizers. A simulation study is carried out to examine the numerical performance of the proposed tests.