Problems in Model Selection, Mixtures and Weighted Likelihood

模型选择、混合和加权似然中的问题

• 批准号: 0072319
• 负责人: Marianthi Markatou
• 金额: $ 9.8万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072319&HistoricalAwards=false
• 关键词: Problems; Model; Selection; Mixtures; Weighted

AbstractProblems in model selection, mixtures and weighted likelihoodWe study problems in model selection, mixtures and weighted likelihood. In particular, we first discuss extensions of the weighted likelihood methodology introduced by Markatou et al (1997,1998) in the context of regression models and its connection to model selection issues with emphasis in the mixture model context. We then generalize these ideas to study general model selection problems. The role of the disparity measures that are associated with weighted likelihood, and several others, is studied in detail in connection with goodness of fit approach to model selection.The point of view we take here is that parametric models can provide informative, parsimonious descriptions of the data. Then, the test statistics for testing the model adequacy are constructed and the asymptotic distributions under the null hypothesis and under contiguous alternatives are studied. The theory here is based on empirical processes. To practically implement the methods we propose to bootstrap the test statistics to obtain appropriate p-values. We consider bootstrapping from a hybrid between the model distribution stipulated by the null hypothesis and the data and study the consistency of it. When the model is false we prefer nonparametric bootstrap. The performance of Bickel's m out of n bootstrap will be examined.

模型选择、混合与加权似然问题本文研究了模型选择、混合与加权似然问题。 特别是，我们首先讨论了Markatou等人（1997，1998）在回归模型的背景下引入的加权似然方法的扩展及其与混合模型背景下的模型选择问题的联系。 然后，我们推广这些想法来研究一般的模型选择问题。 与加权似然相关的差异度量的作用，以及其他几个，详细研究了与拟合优度方法模型selection.The点，我们在这里采取的是，参数模型可以提供翔实的，简约的数据描述。 然后，构造了检验模型充分性的检验统计量，并研究了在原假设和相邻方案下的渐近分布。 这里的理论是基于经验过程的。 为了实际实现的方法，我们建议自举测试统计量，以获得适当的p值。 我们考虑从零假设所规定的模型分布和数据之间的混合自举，并研究它的一致性，当模型为假时，我们倾向于非参数自举。 将检查Bickel的m out of n bootstrap的性能。