论文标题
测试异性疾病下的许多限制
Testing Many Restrictions Under Heteroskedasticity
论文作者
论文摘要
我们提出了一个假设检验，该测试允许在异性线性回归模型中进行许多测试的限制。该测试将常规F统计量与纠正许多限制和条件异方差纠正的临界值进行了比较。该更正使用剩余的估计，将临界价值和保留估算正确置于适当的扩展。测试的较大样本特性是在渐近框架中建立的，在渐近框架中，测试限制的数量可以固定或可能随样本量而生长，甚至可以与观测值成正比。我们表明，该测试是渐近有效的，并且在后者有效时具有与确切的F检验相同的局部替代方案的非平凡渐近功率。模拟证实了这些理论发现，即使在强烈的异性恋性下，也表明了中等小样本中的尺寸控制。
We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.
