WEAK-IDENTIFICATION ROBUST WILD BOOTSTRAP APPLIED TO A CONSISTENT MODEL SPECIFICATION TEST
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用于一致模型设定检验的弱识别稳健野生自助法
- 研究问题
- 当备择下存在干扰参数，且部分参数可能弱识别或不识别时，如何构造同时控制检验水平并保持一致性的模型设定检验？
- 方法与思路
- 作者针对不同识别情形计算野生自助法 p 值，再合并极端识别情形的结果，并对稳健 p 值进行平滑以构造检验。
- 材料陈述的贡献
- 摘要称平滑检验在各类识别程度下具有正确渐近水平、一致性和一致水平控制；其中一种检验在所报告模拟中表现较好。
- 阅读关注点
- 应核对识别情形的划分、p 值合并与平滑规则、一致水平控制的参数范围，以及为何常见上确界和平均统计量仍有困难。
- 阅读边界
- 仅依据所给 Crossref 摘要；具体条件、平滑参数和模拟数值未说明，模拟中的优势不能视为普遍支配，也不能推断刊本变化。
原文摘要
We present a new robust bootstrap method for a test when there is a nuisance parameter under the alternative, and some parameters are possibly weakly or nonidentified. We focus on a Bierens (1990, Econometrica 58, 1443–1458)-type conditional moment test of omitted nonlinearity for convenience. Existing methods include the supremum p -value which promotes a conservative test that is generally not consistent, and test statistic transforms like the supremum and average for which bootstrap methods are not valid under weak identification. We propose a new wild bootstrap method for p -value computation by targeting specific identification cases. We then combine bootstrapped p -values across polar identification cases to form an asymptotically valid p -value approximation that is robust to any identification case. Our wild bootstrap procedure does not require knowledge of the covariance structure of the bootstrapped processes, whereas Andrews and Cheng’s (2012a, Econometrica 80, 2153–2211; 2013, Journal of Econometrics 173, 36–56; 2014, Econometric Theory 30, 287–333) simulation approach generally does. Our method allows for robust bootstrap critical value computation as well. Our bootstrap method (like conventional ones) does not lead to a consistent p -value approximation for test statistic functions like the supremum and average. Therefore, we smooth over the robust bootstrapped p -value as the basis for several tests which achieve the correct asymptotic level, and are consistent, for any degree of identification. They also achieve uniform size control. A simulation study reveals possibly large empirical size distortions in nonrobust tests when weak or nonidentification arises. One of our smoothed p -value tests, however, dominates all other tests by delivering accurate empirical size and comparatively high power.