This paper proposes a new overidentifying restrictions test in a linear model when the number of instruments (possibly weak) may be smaller or larger than the sample size n or even infinite in a heteroskedastic framework. The proposed J test combines two techniques: the Jackknife method and the regularization technique which consists in stabilizing the projection matrix. We theoretically show that our new test achieves the asymptotically correct size in the presence of many instruments. The simulation results demonstrate that our modified J statistic test has better empirical properties in small samples than existing J tests. We also propose a regularized F-test to assess the strength of the instruments, which is robust to heteroskedasticity and many instruments.

中文翻译：

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使用正则化 Jackknife IV 测试对多种工具的过度识别限制和异方差性

本文提出了一种新的线性模型中的过度识别限制测试，当工具的数量（可能很弱）可能小于或大于样本量n 时，甚至在异方差框架中甚至是无穷大。提议的J测试结合了两种技术：Jackknife 方法和包括稳定投影矩阵的正则化技术。我们从理论上表明，我们的新测试在存在许多仪器的情况下实现了渐近正确的大小。仿真结果表明，我们改进的J统计检验在小样本中比现有的J具有更好的经验特性测试。我们还提出了一个正则化的 F 检验来评估工具的强度，它对异方差性和许多工具都具有鲁棒性。