Rotation tests
Rotation tests
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DOI：
10.1007/s11222-005-4789-5
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发表时间：
2005-01-01
影响因子：
2.2
通讯作者：
Langsrud, O
中科院分区：
文献类型：
--
作者：
Langsrud, O
本文描述了一个通用的框架，做蒙特卡罗测试多元线性回归。旋转方法假设多元正态性，是经典多元检验的真正概括-任何可以想象的检验统计量都是允许的。广义检验统计量取决于未知协方差矩阵。旋转检验通过充分的统计量来处理这个问题，与置换检验相比，我们用适当的随机旋转来代替置换。置换检验避免了多正态假设，但它们仅限于相对简单的模型。另一方面，旋转检验尤其适用于单变量F检验的任何多变量推广。作为一个重要的应用，详细描述了如何对每个单个响应p值进行多重性非保守调整。这种方法是精确和非保守的（不像Bonferroni），它是普通F检验的推广（除了通过模拟计算）。因此，本文提供了一个精确的Monte Carlo解决方案的经典问题的多重测试。
This paper describes a generalised framework for doing Monte Carlo tests in multivariate linear regression. The rotation methodology assumes multivariate normality and is a true generalisation of the classical multivariate tests-any imaginable test statistic is allowed. The generalised test statistics are dependent on the unknown covariance matrix. Rotation testing handles this problem by conditioning on sufficient statistics.Compared to permutation tests, we replace permutations by proper random rotations. Permutation tests avoid the multinormal assumption, but they are limited to relatively simple models. On the other hand, a rotation test can, in particular, be applied to any multivariate generalisation of the univariate F-test.As an important application, a detailed description of how each single response p-value can be non-conservatively adjusted for multiplicity is given. This method is exact and non-conservative (unlike Bonferroni), and it is a generalisation of the ordinary F-test (except for the computation by simulations). Hence, this paper offers an exact Monte Carlo solution to a classical problem of multiple testing.