Efficient Tests in the Presence of Nuisance Parameters under the Null Hypothesis

时间序列数据通常只包含有关感兴趣的经济现象的有限信息。因此，为了了解这些现象，必须依赖（至少近似地）有效的推理过程。在具有非标准渐近理论的模型中，有效的检验通常必须从第一性原理推导出来。这在零假设下存在干扰参数时尤其困难，然而许多模型和推理问题属于这一类。该项目旨在开发一套通用的工具和参数，允许在这样的环境中构造渐近有效的测试。提出了一种算法来数值确定参数小样本设置中的测试，这种测试在其功率明显接近所有测试功率的上界的意义上几乎是有效的。这种小样本效率随后被证明转化为某些测试的渐近效率性质。通过两个初步应用说明了该方法的实用性和可行性。第一个是关于双变量设置中协整向量值的推断，当常见的随机趋势遵循一般的持续过程时，它将通常的I(1)假设嵌入为特殊情况。第二个应用程序旨在开发测试，有效地区分参数不稳定性的单一移位形式和随机行走型进化。该研究项目为计量经济学理论中的教科书问题提供了一条前进的道路，具有许多潜在的应用前景。它的贡献是在概念和计算水平上，并且，在这两个已完成的应用中，应用研究人员直接感兴趣。更广泛的影响：虽然确定（几乎）有效的测试涉及到数值，但这项工作只需要对任何模型和问题进行一次。对数据的应用是完全直接的，这应该有助于实证研究人员的广泛采用。该项目的想法和结果将通过在大学和会议上的演讲以及免费提供的计算机代码来传播。最后，通过与研究生和研究助理的合作，该提案对学生培训有直接影响

Time series data often contain only limited information about economic phenomena of interest. In order to learn about these phenomena, one must therefore rely on (at least approximately) efficient inference procedures. In models with nonstandard asymptotic theory, efficient tests must typically be derived from first principles. This is especially difficult in the presence of nuisance parameters under the null hypothesis, yet many models and inference problems fall into this category. This project aims at developing a general set of tools and arguments that allow the construction of asymptotically efficient tests in such an environment. An algorithm is suggested to numerically determine tests in a parametric small sample setting that are almost efficient in the sense that their power comes demonstrably close to an upper bound on the power of all tests. This small sample efficiency is then shown to translate into an asymptotic efficiency property of certain tests. The relevance and feasibility is illustrated by two preliminary applications. The first concerns inference about the value of the cointegrating vector in a bivariate set-up when the common stochastic trend follows a general persistent process, which embeds the usual I(1) assumption as a special case. The second application seeks to develop tests that efficiently discriminate between a single shift form of parameter instability from a random walk-type evolution.The research project suggests a way forward on a textbook problem in econometric theory, with numerous potential applications. Its contribution is both on a conceptual and computational level, and, in the two worked-out applications, of immediate interest to applied researchers.Broader Impacts: Although the determination of (almost) efficient tests is numerically involved, this work only needs to be done once for any model and problem. The application to data is entirely straightforward, which should facilitate a widespread adoption by empirical researchers. The project's ideas and results will be disseminated through presentations at universities and conferences, as well as freely available computer code. Finally, through collaborations with graduate students and research assistants, the proposal has a direct impact on student training