This paper extends validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003) to instrumental variable regression models with unknown error variance and many weak instruments. In this setting, we argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that this modified test achieves asymptotic validity under many weak instrument asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003). A simulation study illustrates the desirable properties of our test.

翻译：本文将莫雷拉(2003年)开发的有条件概率比(CLR)测试的有效性延伸至具有未知误差差异和许多薄弱仪器的辅助性可变回归模型。 在这种背景下,我们争辩说,具有估计误差差异的常规CLR测试会失去精确的相似性,并且几乎是无效的。我们为具有估计误差差异的概率比(LR)统计建议了一个修改的关键值功能,并证明这一修改的测试在许多薄弱仪器无症状下取得了无症状有效性。我们的关键值功能是通过使用四种统计数据而不是莫雷拉(2003年)的两种统计数据代表LR来构建的。一个模拟研究显示了我们测试的可取性。