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

零假设下存在干扰参数的有效检验

• 批准号: 0751056
• 负责人: Ulrich Mueller
• 金额: $ 16.18万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0751056&HistoricalAwards=false
• 关键词: Efficient; Tests; Presence; Nuisance; Parameters

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

时间序列数据通常仅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，人们必须依赖（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，有效检验通常必须从第一原理中导出。在原假设下存在干扰参数的情况下，这尤其困难，但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论据，允许在这样的环境中构建渐近有效的测试。建议采用一种算法来在参数小样本设置中以数字方式确定测试，这些测试几乎是有效的，因为它们的功效明显接近所有测试功效的上限。然后，这种小样本效率被证明可以转化为某些测试的渐近效率特性。两个初步应用说明了相关性和可行性。第一个涉及当共同随机趋势遵循一般持续过程时对双变量设置中协整向量值的推断，该过程将通常的 I(1) 假设嵌入为特例。第二个应用旨在开发能够有效地区分参数不稳定性的单移形式和随机游走型演化的测试。该研究项目提出了一种解决计量经济学理论教科书问题的方法，具有许多潜在的应用。它的贡献既在概念层面又在计算层面，并且在两个已制定的应用程序中，引起了应用研究人员的直接兴趣。 更广泛的影响：虽然在数字上涉及（几乎）有效测试的确定，但这项工作只需要对任何模型和问题进行一次。数据的应用完全简单，这应该有助于实证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，该提案对学生培训产生了直接影响