On the Relative Robustness of the Size of Tests to Local Model Violations

关于局部模型违规测试规模的相对鲁棒性

• 批准号: 1346827
• 负责人: Patrik Guggenberger
• 金额: $ 8.13万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1346827&HistoricalAwards=false
• 关键词: Relative; Robustness; Size; Tests; Local

When an applied researcher tests a hypothesis, she can make one of two mistakes. She can reject a true null hypothesis or accept a false one. To implement the test the applied researcher picks a significance level, which is the maximal probability at which the researcher is willing to commit the first type of error. This maximal probability at which the first error occurs is also called the size of the test.Competing testing procedures of equal (large sample) size are typically ranked according to their relative power properties, where power denotes 1 minus the probability of the second type of error. However, noting that key assumptions underlying Econometric models are often questionable in practice, the PI proposes an alternative ranking of tests according to their relative large sample size distortion under local violations of certain model assumptions. The PI includes tests into the comparison that have large sample size equal to nominal size when the key model assumptions hold true and that are consistent against fixed alternatives when the model is point identified. As a more ambitious goal--beyond ranking existing tests according to the new measure--the PI intends to investigate whether there exists an optimal test, that is, a test that has smallest large sample size distortion for a given degree of local violations of the model assumptions in the class of tests that have correct asymptotic size when the model assumptions are true and are consistent when the model is point identified.Out of many examples, the PI focuses on two lead examples. First, the PI considers hypothesis tests involving the structural parameter vector in the linear instrumental variables (IVs) model where the IVs and the structural error term may be correlated. The correlation fades away at rate n^(-1/2) as the sample size n increases to infinity. The PI considers tests that have correct large sample size when the correlation is in fact zero and that are consistent when the IVs are strong and uncorrelated with the error term. Of the various tests considered the PI finds that Anderson-and-Rubin-type tests are the least distorted under local correlation of the IVs and the error term.Second, the PI considers tests for the unknown parameter vector in partially identified models defined by moment inequalities. The PI ranks the tests with respect to their large sample size distortion when the moment inequalities are locally violated at rate n^(-1/2). The PI finds that among the tests considered those based on plug-in asymptotic critical values are the least size distorted under local misspecification. An optimality theory is under investigation for both examples.Borader Impact: If an applied researcher chooses a test based on its favorable power properties, then her inference may suffer from severe size distortion when the model assumptions are slightly violated. Unfortunately, model violations seem to be pervasive in empirical applications. The new criterion instead suggests using tests that limit the size distortion while still being consistent under standard assumptions. The proposed methods will have broad empirical impact and has the potential to improve inference. It is expected that the methods provided by this research will find frequent use by applied researchers in social sciences within academia and the public sector.

当一个应用研究者测试一个假设时，她可能会犯两个错误之一。 她可以拒绝真实的零假设，也可以接受虚假的零假设。为了实施测试，应用研究人员选择了一个显著性水平，这是研究人员愿意犯第一类错误的最大概率。第一个错误发生的最大概率也称为测试的大小。相同（大样本）大小的竞争测试程序通常根据其相对功效属性进行排名，其中功效表示1减去第二类错误的概率。然而，注意到计量经济学模型的关键假设在实践中往往是有问题的，PI提出了一个替代排名的测试，根据其相对较大的样本量失真的局部违反某些模型假设。PI将检验纳入比较，当关键模型假设成立时，大样本量等于标称量，当模型为点识别时，与固定替代方案一致。作为一个更雄心勃勃的目标--除了根据新的衡量标准对现有的测试进行排名之外--PI打算调查是否存在一个最佳测试，也就是说，在模型假设为真时具有正确渐近大小且模型为点识别时具有一致性的检验类别中，对于给定程度的模型假设局部违反，具有最小大样本量失真的检验。举例来说，PI侧重于两个领先的例子。首先，PI考虑涉及线性工具变量（IV）模型中结构参数向量的假设检验，其中IV和结构误差项可能相关。当样本大小n增加到无穷大时，相关性以n^（-1/2）的速率衰减。PI考虑当相关性实际上为零时具有正确的大样本量的检验，以及当IV较强且与误差项不相关时具有一致性的检验。在各种测试中，PI发现安德森和鲁宾型测试在IV和误差项的局部相关性下是最不失真的。其次，PI考虑由矩不等式定义的部分识别模型中未知参数向量的测试。 当矩不等式以n^（-1/2）的速率被局部违反时，PI根据测试的大样本量失真对测试进行排名。 PI发现，在被认为是那些基于插件的渐近临界值的测试是最小的尺寸扭曲下的局部误指定。Borader Impact：如果一个应用研究者选择了一个基于其有利的功效属性的测试，那么当模型假设稍微被违反时，她的推断可能会受到严重的尺寸失真。不幸的是，模型违反似乎是普遍的经验应用。相反，新标准建议使用限制尺寸失真的测试，同时在标准假设下仍然保持一致。所提出的方法将具有广泛的经验影响，并有可能改善推理。预计本研究提供的方法将经常被学术界和公共部门的社会科学应用研究人员使用。