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，必须依靠(至少是近似地)有效的推理程序。在具有非标准渐近理论的模型中，有效的检验通常必须源自第一原理。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。这个项目的目的是开发一套通用的工具和论点，以便在这样的环境中构建渐近有效的测试。提出了一种在参数小样本环境下确定检验的算法，该算法几乎是有效的，因为它们的功率明显地接近所有检验的功率的上界。然后，这种小样本效率被证明为某些检验的渐近效率性质。通过两个初步应用，说明了该方法的相关性和可行性。第一种是关于一般随机趋势服从一般持续过程的二元模型中协积分向量的值的推论，通常的I(1)假设是其特例。第二个应用寻求开发测试，有效地区分参数不稳定性的单一转移形式和随机游动类型的演化。研究项目为计量经济学理论中的一个教科书问题提出了一条前进的方向，具有许多潜在的应用。它的贡献既是在概念层面上的，也是在计算层面上的，并且在两个已完成的应用程序中，应用研究人员立即感兴趣。广泛的影响：尽管确定(几乎)有效的测试在数值上是涉及到的，但对于任何模型和问题，这项工作只需要做一次。对数据的应用是完全直截了当的，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陈述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，该提案对学生的培训产生了直接影响

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