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。为了了解这些现象，人们必须依赖（至少近似）有效的推理程序。在具有非标准渐近理论的模型中，有效检验通常必须从第一原理导出。这在零假设下存在干扰参数的情况下尤其困难，然而许多模型和推理问题都属于这一类。 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建渐近有效的测试。一种算法建议，以数值确定测试的参数小样本设置，几乎是有效的意义上说，他们的权力来证明接近的上限的所有测试的权力。这种小样本的效率，然后转化为一个渐进的效率属性的某些测试。两个初步的应用说明了相关性和可行性。第一个问题是当共同的随机趋势遵循一个一般的持续过程时，在一个双变量集合中关于协整向量值的推断，该过程嵌入了通常的I（1）假设作为特殊情况。第二个应用程序旨在开发测试，有效区分参数不稳定性的一个单一的移位形式从随机行走型evolution.The研究项目提出了一种方法，在计量经济学理论的教科书问题，具有许多潜在的应用。它的贡献是在概念和计算水平上，并在两个制定的应用程序，立即感兴趣的应用researchers.Broader影响：虽然确定（几乎）有效的测试是数字参与，这项工作只需要做一次任何模型和问题。数据的应用是完全简单的，这应该有助于经验研究人员的广泛采用。该项目的想法和成果将通过在大学和会议上的介绍以及免费提供的计算机代码传播。最后，通过与研究生和研究助理的合作，该提案对学生培养产生了直接影响

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