摘要翻译：
在检验回归模型中误差的相关性时，对于强相关性的误差，检验的功率可能很低。这种违反直觉的现象被称为“零功率陷阱”。尽管有大量的文献致力于这一问题，主要集中在其检测上，但尚未找到令人信服的解决方案。本文首先讨论了零功率陷阱现象的理论结果。然后，我们建议并比较了三种避免它的方法。给定一个遭受零功率陷阱的初始测试，我们推荐用于实践的方法导致一个修改的测试，当相关性变得非常强时，其功率收敛到1。此外，改进的检验具有与初始检验近似相同的幂函数，从而近似地保持了它的所有最优性性质。我们还提供了一些在测试网络产生的相关性的背景下的数值例子。
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英文标题：
《How to avoid the zero-power trap in testing for correlation》
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作者：
David Preinerstorfer
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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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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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  In testing for correlation of the errors in regression models the power of tests can be very low for strongly correlated errors. This counterintuitive phenomenon has become known as the "zero-power trap". Despite a considerable amount of literature devoted to this problem, mainly focusing on its detection, a convincing solution has not yet been found. In this article we first discuss theoretical results concerning the occurrence of the zero-power trap phenomenon. Then, we suggest and compare three ways to avoid it. Given an initial test that suffers from the zero-power trap, the method we recommend for practice leads to a modified test whose power converges to one as the correlation gets very strong. Furthermore, the modified test has approximately the same power function as the initial test, and thus approximately preserves all of its optimality properties. We also provide some numerical illustrations in the context of testing for network generated correlation.
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PDF链接：
https://arxiv.org/pdf/1812.10752