Mathematical Sciences: Parametric and Nonparametric Likelihood Studies

拟议的研究是针对一些主题在该地区的可能性为基础的统计方法。一组主题将涉及在参数模型领域的几个新的渐近方法的发展，重点是在滋扰参数和测试方法的混合物中的组件的数量存在的改进的分布特性。第二组主题围绕混合模型中的半参数和非参数推断，其中模型类需要扩展，并需要开发进一步的推断方法。 最广泛使用的得出统计结论的方法，称为最大似然法，是基于一个直观概念的数学版本，即参数的真实值通常会在给定观测数据的那些似乎“最有可能”的参数中找到。这个强大的工具使人们能够写下复杂现象的模型，并通过最大限度地提高可能性，得出有关生成数据的自然状态的结论。然而，似然方法并不完美，本研究提案的目的是在计算和理论方面，在几个广泛应用的领域进一步发展。

The proposed research is directed towards a number of topics in the area of likelihood based statistical methods. One set of topics will involve the development of several new asymptotic methods in the area of parametric models, focussing on improved distributional properties in the presence of nuisance parameters and on testing methods for the number of components in a mixture. The second set of topics revolves around semiparametric and nonparametric inference in the mixture model, where the class of models needs to be expanded and further inferential methods need to be developed. The most widely used method for drawing statistical conclusions, called the method of maximum likelihood, is based on a mathematical version of the intuitive notion that the true value of a parameter will generally be found among those that seem "most likely" given the observed data. This powerful tool enables one to write down models for complex phenomenon and, by maximizing the likelihood, draw conclusions about the state of nature that generated the data. However, the likelihood method is not perfect, and the objective of this research proposal is to further its development, both in computation and in theory, in several areas of wide application.