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摘要翻译：
在异方差线性回归模型中，我们提出了一个允许许多被检验限制的假设检验。该测试将传统的F统计量与修正许多限制和条件异方差的临界值进行比较。该校正利用留一估计来正确地居中临界值，留三估计来适当地缩放临界值。检验的大样本性质是在一个渐近框架中建立的，在这个框架中，被检验的限制数可以是固定的，或者可以随着样本大小增长，甚至可以与观察次数成正比。当精确F检验有效时，我们证明了该检验是渐近有效的，并且对与精确F检验相同的局部方案具有非平凡的渐近幂。模拟证实了这些理论发现的相关性，并表明在中等小的样品中，在强异方差下，尺寸控制也很好。
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英文标题：
《Testing Many Restrictions Under Heteroskedasticity》
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作者：
Stanislav Anatolyev, Mikkel S{\o}lvsten
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最新提交年份：
2021
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
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. The correction utilizes leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. 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 the relevance of these theoretical findings and suggest excellent size control in moderately small samples also under strong heteroskedasticity.
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PDF链接：
https://arxiv.org/pdf/2003.07320
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