We develop a new permutation test for inference on a subvector of coefficients in linear models. The test is exact when the regressors and the error terms are independent. Then, we show that the test is asymptotically of correct level, consistent and has power against local alternatives when the independence condition is relaxed, under two main conditions. The first is a slight reinforcement of the usual absence of correlation between the regressors and the error term. The second is that the number of strata, defined by values of the regressors not involved in the subvector test, is small compared to the sample size. The latter implies that the vector of nuisance regressors is discrete. Simulations and empirical illustrations suggest that the test has good power in practice if, indeed, the number of strata is small compared to the sample size.

翻译：我们提出了一种新的置换检验方法，用于线性模型中系数子向量的推断。当回归变量与误差项相互独立时，该检验是精确的。随后我们证明，在放宽独立性条件的情况下，该检验在渐近意义上具有正确的显著性水平、一致性，并能检测局部备择假设的检验功效，这需满足两个主要条件：第一是对回归变量与误差项之间通常无相关性条件的轻微强化；第二是未参与子向量检验的回归变量取值所定义的分层数相对于样本量较小——这意味着冗余回归变量向量为离散型。模拟与实证分析表明，当分层数确实远小于样本量时，该检验在实际应用中具有良好的检验功效。