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，用于对线性模型中系数子向量进行推断。当回归变量与误差项相互独立时，该检验是精确成立的。随后我们证明，在放松独立性条件时，该检验在两种主要条件下渐近具有正确的显著性水平、一致性且对局部备择假设具有检验功效。第一个条件是对回归变量与误差项通常无相关性的轻微强化。第二个条件是：由子向量检验未涉及的回归变量取值定义的层数，相对于样本量较小。后者意味着干扰回归变量向量是离散的。模拟与实证案例表明，当层数确实相对于样本量较小时，该检验在实践中具有良好的检验功效。