Problems in Model Selection, Mixtures and Weighted Likelihood

摘要模型选择、混合和加权似然问题我们研究了模型选择、混合和加权似然问题。特别是，我们首先讨论了Markatou等人(1997,1998)在回归模型背景下引入的加权似然方法的扩展，以及它与混合模型背景下的模型选择问题的联系。然后，我们将这些思想推广到研究一般的模型选择问题。结合模型选择的拟合优度方法，详细研究了与加权似然相关的视差度量以及其他几种方法的作用。我们的观点是，参数模型可以提供对数据的信息性、简约性描述。在此基础上，构造了检验模型充分性的检验统计量，并研究了零假设和相邻备选方案下的渐近分布。这里的理论是基于经验过程的。为了实际实现这些方法，我们建议对测试统计量进行引导，以获得适当的p值。我们考虑了从零假设所规定的模型分布与数据的混合中自举，并研究了它的一致性。当模型为假时，我们倾向于非参数自举。将检查Bickel的m of n自举的性能。

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.