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

协作研究：有限非参数混合物的估计、推理和计算

• 批准号: 1208994
• 负责人: Michael Levine
• 金额: $ 8.65万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1208994&HistoricalAwards=false
• 关键词: Collaborative; Research; Estimation; Inference; Computation

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.

该项目旨在开发理论和方法，以估计非参数多元有限混合物中的功能成分和权重。这些混合物仅假定这些组件是从某些无参数规范的多元密度函数家族中汲取的。研究人员已经活跃于这一新兴研究领域，并适应了许多估计方法，这些估计方法从有限的参数混合理论已知到非参数环境。 PI和Co-Pi提出了许多可行和快速的算法，这些算法可用于计算实践中所得的估计器。最后，两个研究人员都展示了如何为提出的估计器获得大样本渐近结果。限定分布的非参数混合物可以为许多实际重要的问题提供答案。例如，如果有许多可能的诊断，它们可用于帮助医生确定确定的诊断。这种情况的一个例子是患有可能心脏病发作的患者，在其他鉴别诊断中也是可能的。发展心理学提供了另一个有用的例子。实际上，还可以使用这些混合物轻松地对儿童认知发展进行研究，特别是鉴定儿童用于完成各种任务的策略。这对发展心理学具有重要意义，为儿童心理学家所面临的许多困难问题提供答案，同时帮助儿童以最佳方式成熟并发展。 PI和Co-Pi提出了许多有效算法来估计这些混合物并完成上述实际任务。这些算法将是公开可用的，易于用作称为MixTools的R软件包的一部分。