EXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS
EXACT AND ASYMPTOTICALLY ROBUST PERMUTATION TESTS
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DOI：
10.1214/13-aos1090
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发表时间：
2013-04-01
影响因子：
4.5
通讯作者：
Romano, Joseph P.
中科院分区：
文献类型：
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作者：
Chung, EunYi;Romano, Joseph P.
在给定来自P和Q的独立样本的情况下，当零假设为P=Q时，两样本置换检验允许构造精确的水平检验。另一方面，当比较或测试P和Q的特定参数，例如它们的均值或中值时，置换检验不需要是水平a，甚至在大样本中不需要接近水平α。在比较估计的非常弱的假设下，我们给出了一个一般的检验方法，即当基本分布相同时，置换检验的渐近有效性成立，同时在有限样本中保持精确的拒绝概率α。这些思想具有广泛的适用性，并特别注意比较一般参数的k样本问题，由此构造了一个置换检验，该检验在相同分布的假设下是精确水平α，但在更一般的参数相等的零假设下具有渐近拒绝概率α。并进行了蒙特卡罗模拟研究。基于耦合结构以及多项式和多元超几何分布的一个关键的邻接性论证，一个非常普遍的理论是可能的。
Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P = Q. On the other hand, when comparing or testing particular parameters theta of P and Q, such as their means or medians, permutation tests need not be level a, or even approximately level alpha in large samples. Under very weak assumptions for comparing estimators, we provide a general test procedure whereby the asymptotic validity of the permutation test holds while retaining the exact rejection probability alpha in finite samples when the underlying distributions are identical. The ideas are broadly applicable and special attention is given to the k-sample problem of comparing general parameters, whereby a permutation test is constructed which is exact level alpha under the hypothesis of identical distributions, but has asymptotic rejection probability alpha under the more general null hypothesis of equality of parameters. A Monte Carlo simulation study is performed as well. A quite general theory is possible based on a coupling construction, as well as a key contiguity argument for the multinomial and multivariate hypergeometric distributions.