论文标题
更有效的精确组不变测试：使用代表性亚组
More Efficient Exact Group-Invariance Testing: using a Representative Subgroup
论文作者
论文摘要
基于置换，旋转或弹性板的非参数测试是组差异测试的示例。这些测试在代数意义上的一组具有组结构的转换下测试无效分布的不变性。这样的组通常是巨大的，这使得在计算上使用整个组都无法进行测试。因此，使用该组随机采样的转换集测试是标准实践。该随机样本仍然需要大量才能获得良好的功率和可复制性。我们通过使用精心设计的转换子组而不是随机样本来改进这种标准实践。所得的亚组不变性测试仍然是精确的，因为一个组下的不变性意味着其子组下的不变性。 我们在广义位置模型中说明了这一点，并根据相同数量的转换获得了更强大的测试。特别是，我们表明，与基于随机样本的测试相比，信噪比较低的亚组不变测试是一致的。对于普通位置模型的特殊情况和子组的特殊设计，我们表明功率提高等效于蒙特卡洛$ z $ - 检验和蒙特卡洛$ t $ -test之间的功率差。
Non-parametric tests based on permutation, rotation or sign-flipping are examples of group-invariance tests. These tests test invariance of the null distribution under a set of transformations that has a group structure, in the algebraic sense. Such groups are often huge, which makes it computationally infeasible to test using the entire group. Hence, it is standard practice to test using a randomly sampled set of transformations from the group. This random sample still needs to be substantial to obtain good power and replicability. We improve upon this standard practice by using a well-designed subgroup of transformations instead of a random sample. The resulting subgroup-invariance test is still exact, as invariance under a group implies invariance under its subgroups. We illustrate this in a generalized location model and obtain more powerful tests based on the same number of transformations. In particular, we show that a subgroup-invariance test is consistent for lower signal-to-noise ratios than a test based on a random sample. For the special case of a normal location model and a particular design of the subgroup, we show that the power improvement is equivalent to the power difference between a Monte Carlo $Z$-test and a Monte Carlo $t$-test.
