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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=686839
• 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，金融或其他行业中，从业人员拥有来自许多相关人群的数据。研究他们的相似性和差异是一个实际重要性的问题。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，经验可能性（EL）方便地利用来自多个人群的所有数据，以提高推断。基于EL的方法具有优雅的大样本属性，用于通过平滑估计功能定义的参数。对于由非平滑函数定义的参数，其中一些属性似乎存在，但缺乏理论上的理由。目前，我们考虑了人口分位数。它们是实际重要性的参数，并且与非平滑估计功能有关。在DRM下，对于非平滑参数，了解EL的大样本特性的任务是该提案中的研究问题之一。******一个分布在另一个提案中的随机优势是财务和经济学的重要概念。必须基于可靠的数据和严格的分析来建立优势。当前的方法采用基于经验分布的简单统计数据，这些分布留出了改进的空间。 EL-DRM组合应为财务研究人员提供更简单，更有效的推理工具。我们将这项任务称为本提案中的另一个示例研究问题。******有限混合物在我以前的建议中占据了重要地位，并且在统计研究中仍然占据了很大的领域。该EM测试在这里获得了一些基础，但由于有限的回归混合物和隐藏的Markov模型，它缺乏其他非规范模型的巨大力量。该提议相信可以使EM测试同样强大。但是，我们必须研究一些详细信息，以使这个想法在应用程序中起作用。为所有这些模型开发EM测试将是很多工作。******在回归混合物中，人们可能对某些特定解释变量的效果的重要性感兴趣。在这种情况下，研究人员也可能对解释变量感兴趣，即使它们仅在少数（尽管不是全部）亚群中产生重大影响。如果已知亚群的数量，则可能将可能比率测试直接应用于回归混合物中的数据。但是，知道回归混合物的顺序更是一个例外，而不是常规。在大多数情况下，由于数据量有限，很难以令人满意的确定性确定混合物的顺序。可辩护的假设检验程序必须考虑这种不确定性。在假设检验中适应秩序不确定性的问题引起了人们的关注。该建议计划使用基准类型的方法研究此问题。