Collaborative Research: Estimation, Inference, and Computation for Finite Nonparametric Mixtures

本计画旨在发展非参数多元有限混合物中函数分量与权重之估计理论与方法。这些混合物只假设成分是从一些家庭的多元密度函数，没有任何参数规格。研究人员，谁已经活跃在这一新兴领域的研究，适应了一些估计方法，是已知的有限参数混合理论的非参数背景下。PI和co-PI提出了许多实际可行的快速算法，可用于计算实际中得到的估计量。最后，两个调查显示如何获得大样本的渐近结果所提出的estimations.Finite非参数混合分布可以提供答案，许多实际上重要的问题。例如，它们可以用于帮助医生在具有许多可能诊断的复杂医疗状况的情况下建立明确的诊断。这种情况的一个例子是一个可能的心脏病发作的病人，其中其他鉴别诊断也是可能的。发展心理学提供了另一个有用的例子。事实上，儿童认知发展的研究，特别是儿童完成各种任务所使用的策略的识别，也可以很容易地使用这些混合模型。这对发展心理学具有重要意义，为儿童心理学家面临的许多难题提供了答案，同时帮助儿童以最佳方式成熟和发展。PI和co-PI提出了一些有效的算法来估计这些混合物，并完成上述实际任务。这些算法将作为R软件包mixtools的一部分公开提供，并且易于使用。

This project aims to develop theory and methods for estimation of the functional components and weights in the nonparametric multivariate finite mixtures. These mixtures only assume that the components are drawn from some family of multivariate density functions without any parametric specification. The investigators, who are already active in this emerging area of research, adapt a number of estimation methods that are known from finite parametric mixture theory to the nonparametric context. The PI and the co-PI propose a number of practically feasible and fast algorithms that can be used to compute the resulting estimators in practice. Finally, both investigators show how to obtain large-sample asymptotic results for the proposed estimators.Finite nonparametric mixtures of distributions can provide answers to many practically important questions. As an example, they can be used to help a physician in establishing the definitive diagnosis in case of a complex medical condition with a number of possible diagnoses. An example of such a situation is a patient with a possible heart attack where other differential diagnoses are also possible. Developmental psychology provides another useful example. Indeed, study of cognitive development in children, in particular identification of strategies used by children to accomplish various tasks, can also be modeled easily using these mixtures. This has important implication for developmental psychology, providing answers to many difficult questions faced by child psychologists while helping children mature and develop in an optimal way. The PI and the co-PI propose a number of efficient algorithms to estimate these mixtures and accomplish the practical tasks mentioned above. These algorithms will be publicly available and easy to use as part of the R software package called mixtools.