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，从业者有来自许多相关人群的数据。研究二者的异同是一个具有现实意义的问题。在过去的研究中，我们已经证明密度比模型（DRM）是表征相似度的有效平台。在DRM下，经验似然（EL）可以方便地利用来自多个种群的所有数据进行有效的推理。基于EL的方法对于光滑估计函数定义的参数具有良好的大样本特性。对于由非光滑函数定义的参数，这些性质中的一些似乎保留了下来，但缺乏理论证明。现在，我们考虑的是人口分位数。它们是具有实际意义的参数，与非光滑估计函数有关。理解非光滑参数DRM下电晶体的大样本特性是本课题的研究课题之一。一种分布相对于另一种分布的随机优势是金融学和经济学中的一个重要概念。主导地位必须建立在可靠的数据和严格的分析基础上。目前的方法采用基于经验分布的简单统计，这留下了改进的余地。EL-DRM组合应该为金融研究人员提供更简单、更有效的推理工具。我们将此任务命名为本提案中的另一个示例研究问题。有限混合在我以前的建议中占有重要的地位，并且在统计研究中仍然占有很大的领域。em测试在这里取得了一些进展，但它对其他非规则模型（如有限回归混合模型和隐马尔可夫模型）缺乏广泛的影响力。这一提议相信，新兴市场测试可以做到同样强大。然而，我们必须弄清楚一些细节，使这个想法在应用中起作用。为所有这些模型开发em测试将需要大量的工作。在回归混合中，人们可能对某些特定解释变量的影响的显著性感兴趣。在这种情况下，研究人员可能会对解释变量感兴趣，即使它们只在少数（尽管不是全部）亚种群中有显著影响。如果亚群的数量是已知的，似然比检验可以直接应用于回归混合的数据。然而，在实践中，知道回归混合的顺序更多的是一个例外，而不是一个常规。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。一个站得住脚的假设检验程序必须考虑到这种不确定性。在假设检验中如何调节阶数的不确定性是一个非常有趣的问题。本提案计划使用基准型方法来研究这个问题。