条件矩不等式模型的渐近精确推断
Asymptotically Exact Inference in Conditional Moment Inequality Models
摘要：
在一般条件下，得到了参数在识别集边界上的条件矩不等式模型的一类Kolmogorov-Smirnov型检验统计量的收敛速度和渐近分布.与其他矩不等式设置相比，收敛速度快于根- $n$，并且渐近分布完全取决于非约束矩。这些结果需要开发新的技术，在矩选择、不规则识别、带宽选择和非标准M估计之间建立联系。使用这些结果，我提出了测试，比现有的方法更强大的选择这个检验统计量的临界值。我量化的功率改进表明，新的测试可以检测到的替代品，收敛到点上确定的一组以更快的速度比现有的方法检测。一项蒙特卡罗研究证实，他们使用的检验和渐近近似在有限样本中表现良好。在一个应用程序的处方药支出的收入与间隔数据的健康和退休研究的回归，置信区域的基础上的新的测试是严格的比那些基于现有的方法。
英文摘要：
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. In contrast to other moment inequality settings, the rate of convergence is faster than root-$n$, and the asymptotic distribution depends entirely on nonbinding moments. The results require the development of new techniques that draw a connection between moment selection, irregular identification, bandwidth selection and nonstandard M-estimation. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A monte carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods.
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