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WEAK-IDENTIFICATION ROBUST WILD BOOTSTRAP APPLIED TO A CONSISTENT MODEL SPECIFICATION TEST
Econometric Theory ( IF 0.8 ) Pub Date : 2020-06-02 , DOI: 10.1017/s0266466620000201
Jonathan B. Hill

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.

中文翻译:

应用于一致模型规范测试的弱识别稳健的 WILD 自举

当备选方案下存在令人讨厌的参数并且某些参数可能很弱或无法识别时,我们提出了一种新的鲁棒自举方法进行测试。我们专注于 Bierens (1990,计量经济学58, 1443–1458) 型省略非线性的条件矩检验,为方便起见。现有的方法包括p- 促进通常不一致的保守测试的值,并测试统计转换,如自举方法在弱识别下无效的上限和平均值。我们提出了一种新的 Wild bootstrap 方法p通过针对特定识别案例的价值计算。然后我们结合自举p- 跨极性识别案例的值以形成渐近有效p对任何识别情况都具有鲁棒性的值近似。我们的狂野 bootstrap 过程不需要知道 bootstrap 过程的协方差结构,而 Andrews 和 Cheng (2012a,计量经济学80, 2153–2211; 2013年,计量经济学杂志173, 36–56; 2014年,计量经济学理论30, 287–333) 模拟方法通常可以。我们的方法也允许进行稳健的引导临界值计算。我们的引导方法(像传统方法一样)不会导致一致的p检验统计函数的值近似值,如最高和平均值。因此,我们平滑了健壮的自举p-值作为几个测试的基础,这些测试达到了正确的渐近水平,并且对于任何程度的识别都是一致的。它们还实现了统一的尺寸控制。一项模拟研究揭示了当出现弱或不可识别时,非稳健测试中可能存在较大的经验尺寸失真。我们的平滑之一p然而,价值检验通过提供准确的经验规模和相对较高的功效来主导所有其他检验。
更新日期:2020-06-02
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