摘要翻译：
在回归间断设计(RDD)中，通常的做法是通过测试在截止点处运行变量密度的连续性来评估设计的可信度，如McCrary(2008)。本文基于G阶统计量，提出了密度在点上连续性的一个近似符号检验，并在两个互补渐近框架下研究了它的性质。在第一个渐近框架中，当样本数n发散到无穷大时，局部的观测数目q是固定的，而在第二个渐近框架中，q随着n发散到无穷大而缓慢地发散到无穷大。在这两个框架下，我们证明了在不超过名义水平的零假设下，我们提出的检验在具有极限拒绝概率的意义上是渐近有效的。更重要的是，该检验易于实现，在比竞争方法更弱的条件下渐近有效，在比其渐近有效性所需的条件更强的条件下显示有限样本有效性。在一个仿真研究中，我们发现近似符号检验在零假设下提供了很好的拒绝概率控制，而在替代假设下保持竞争。最后，我们将我们的测试应用到Lee(2008)的设计中，这是RDD研究在职优势的一个著名应用。
---
英文标题：
《Testing Continuity of a Density via g-order statistics in the Regression
  Discontinuity Design》
---
作者：
Federico A. Bugni and Ivan A. Canay
---
最新提交年份：
2020
---
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。
--

---
英文摘要：
  In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose an approximate sign test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under two complementary asymptotic frameworks. In the first asymptotic framework, the number q of observations local to the cut-off is fixed as the sample size n diverges to infinity, while in the second framework q diverges to infinity slowly as n diverges to infinity. Under both of these frameworks, we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level. More importantly, the test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity. In a simulation study, we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.
---
PDF链接：
https://arxiv.org/pdf/1803.07951