Transformations which preserve exchangeability and application to permutation tests
Transformations which preserve exchangeability and application to permutation tests
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DOI：
10.1080/1048525031000089310
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发表时间：
2003-04-01
影响因子：
1.2
通讯作者：
Commenges, D
中科院分区：
文献类型：
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作者：
Commenges, D
观测值的可交换性是应用排列检验的一个关键条件。我们刻画了线性变换，保持交换，区分二阶矩交换和全球交换，我们也研究非线性变换。当交换矩阵不成立时，人们可以尝试找到一个实现近似交换矩阵的变换;然后可以进行近似置换测试。更具体地说，考虑一个统计量T = phi（Y）;可以找到V，使得（Y）除以波浪号= V（Y）是可交换的，并将T =（φ）除以波浪号（（Y）除以波浪号）。在其他情况下，我们可以满足于波浪号上的（Y）有一个可交换的方差矩阵，我们将其表示为二阶矩交换矩阵。当寻求转换到exchangeries，我们显示的特权作用的残差。我们证明了正态线性模型的精确置换检验是可以构造的。最后提出了基于二阶矩交换的近似排列检验方法。在类内相关模型的情况下，转换很容易实现。我们还给出了线性和二次形式的置换矩，并展示了如何通过Cornish-Fishet展开来使用它。
Exchangeability of observations is a key condition for applying permutation tests. We characterize the linear transformations which preserve exchangeability, distinguishing second-moment exchangeability and global exchangeability; we also examine non-linear transformations. When exchangeability does not hold one may try to find a transformation which achieves approximate exchangeability; then an approximate permutation test can be done. More specifically, consider a statistic T = phi(Y); it may be possible to find V such that (Y) over tilde = V(Y) is exchangeable and to write T = (φ) over tilde((Y) over tilde). In other cases we may be content that (Y) over tilde has an exchangeable variance matrix, which we denote second-moment exchangeability. When seeking transformations towards exchangeability we show the privileged role of residuals. We show that exact permutation tests can be constructed for the normal linear model. Finally we suggest approximate permutation tests based on second-moment exchangeability. In the case of an intraclass correlation model, the transformation is simple to implement. We also give permutational moments of linear and quadratic forms and show how this can be used through Cornish-Fishet expansions.