Theory and Applications of the empirical likelihood and finite mixture model

经验似然和有限混合模型的理论与应用

• 批准号: RGPIN-2019-04204
• 负责人: Chen, Jiahua
• 金额: $ 2.62万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=737480
• 关键词: Theory; Applications; empirical; likelihood; finite

In forestry, finance or other industries, practitioners have data from many related populations. Studying their similarity and difference is a problem of practical importance. In the past, we demonstrated that the density ratio model (DRM) is an effective platform to characterize the similarity. Under DRM, empirical likelihood (EL) conveniently utilizes all data from multiple populations for efficient inference. The EL based methods have elegant large sample properties for the parameters defined by smooth estimating functions. For parameters defined by non-smooth functions, some of these properties seem to stay but are short of theoretical justification. At this moment, we have population quantiles in mind. They are parameters of practical importance and associated with non-smooth estimating functions. The task of understanding large sample properties of the EL under DRM for non-smooth parameters is one of the research problems in this proposal. The stochastic dominance of one distribution over another is an important notion in finance and economics. The dominance has to be established based on reliable data and rigorous analysis. Current approaches employ simple statistics based on empirical distributions which leave rooms for improvement. The EL-DRM combination should provide financial researchers with simpler and more efficient inference tools. We name this task as another example research problem in this proposal. Finite mixtures occupy a significant place in my previous proposals and it still occupies a large territory in statistical research. The EM-test has gained some ground here but it lacks sweeping power for other non-regular models as the finite regression mixture and hidden Markov model. This proposal holds faith that the EM test can be made just as powerful. Yet we must work out some particulars to make the idea work in applications. It will be a lot of work to have EM-test developed for all these models. In regression mixtures, one may be interested in the significance of the effect of some specific explanatory variables. Under this scenario, researchers can be interested in explanatory variables even if they have a significant effect only in a few, though not all, subpopulations. If the number of the subpopulations is known, a likelihood ratio test can be directly applied to data from the regression mixtures. However, knowing the order of the regression mixture is more an exception rather than a routine is in practice. In most cases, with a limited amount of data, it is difficult to determine the order of a mixture with a satisfactory certainty. A defensible hypothesis test procedure must take this uncertainty into consideration. The problem of accommodating the order uncertainty in the hypothesis test is of considerable interest. This proposal plans to study this problem using a fiducial type approach.

在林业、金融或其他行业，从业者拥有来自许多相关人群的数据，研究它们的相似性和差异是一个具有实际重要性的问题。过去，我们证明了密度比模型（DRM）是表征相似性的有效平台。在 DRM 下，经验似然 (EL) 可以方便地利用来自多个群体的所有数据进行有效推理，对于由平滑估计函数定义的参数，其中一些参数具有优雅的大样本属性。特性似乎仍然存在，但缺乏理论依据。目前，我们考虑的是总体分位数，它们是具有实际重要性的参数，并且与非平滑估计函数相关。了解非 DRM 下 EL 的大样本属性的任务。 - 平滑参数是该提案中的研究问题之一。一种分布相对于另一种分布的随机优势是金融和经济学中的一个重要概念。当前的方法必须基于可靠的数据和严格的分析来确定。留下改进空间的经验分布。EL-DRM 组合应该为金融研究人员提供更简单、更实用的推理工具，我们将此任务称为本提案中的另一个示例研究问题，并且在我之前的提案中占有重要地位。 EM 测试在统计研究中仍然占有很大的份额，但它缺乏对其他非正则模型（如有限回归混合和隐马尔可夫模型）的全面影响。​该提案相信 EM 测试。但我们必须弄清楚一些细节才能使这一想法在应用中发挥作用。在回归混合中开发 EM 测试将是一项艰巨的工作。在这种情况下，研究人员可能会对解释变量感兴趣，即使它们仅对少数（尽管不是全部）亚群体产生显着影响。可以直接进行比例测试然而，在实践中，了解回归混合的顺序更多的是一种例外，而不是常规，在数据量有限的情况下，很难确定混合的顺序。具有令人满意的确定性的假设检验程序必须考虑到这种不确定性，该提案计划使用基准类型方法来研究该问题。