Mathematical Sciences: Semiparametric Mixture Models

这项关于混合模型的研究将发展图形诊断和形式检验，以识别广义线性模型中混合的存在，并确定有限混合的混合分量的数量。还将开发方法，以纳入变量有误差的病例对照研究的全部信息。该理论将借鉴非参数最大似然、经验过程、渐近性、凸几何、全正性和模拟的思想和技术。当同质总体以一种丢失个体起源的方式组合在一起时，混合分布就出现了。一个根本的问题涉及确定这种结合是否发生了，如果发生了，有多少不同的起源群体。这项研究将研究图形技术，并将利用数学理论来开发实用的统计方法，以在许多科学应用中回答这类问题。

This research on mixture models will develop graphical diagnostics and formal tests to identify the presence of mixing in generalized linear models and to determine the number of mixing components for finite mixtures. Methods will also be developed to incorporate full information for case-control studies with errors in variables. The theory will draw on ideas and techniques from nonparametric maximum likelihood, empirical processes, asymptotics, convex geometry, total positivity and from simulation. Mixture distributions arise when homogeneous populations are combined in such a way that the origins of individuals are lost. A fundamental problem involves determining whether or not this combining has occurred and if so, how many different originating populations there were. This research will investigate graphical techniques and will use mathematical theory to develop practical statistical methods to answer these kinds of questions in many scientific applications.