Statistical Inference for Complex Data

复杂数据的统计推断

• 批准号: 0400584
• 负责人: Lynne Billard
• 金额: --
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-15 至 2009-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400584&HistoricalAwards=false
• 关键词: Statistical; Inference; Complex; Data

The advent of computers is routinely bringing large, very large datasets for analysis. How to analyze theattendant data and/or how to glean useful information from these data is anything but routine. This proposal investigates two broad areas, viz., mixture decomposition, and regression in the presence of taxonomy and hierarchical variables. The mixture decomposition work is concerned with data in which the observation is a distribution function in the p-dimensional Cartesian product of distributions space, rather than the single point in p-dimensional space of classical data. Such data arise naturally, or after aggregation of original data to a more manageable size yet retaining its inherent information. A goal is to partition these distributions into coherent classes and to estimate the relevant class distributions. It is proposed to adapt ideas from copula theory for classical data, to data comprised of distributions. Embedded in this process is the need to study parameter estimation. Different partitioning techniques will be explored such as dynamical clustering, different measures of fit criterion will be considered, e.g., log-likelihood classification; and different estimation methods explored for the underlying copulas and the associated distributions and their parameters, e.g., maximum likelihood, nonparametric methods such as Parzen's truncated window. The resulting methodology will have wide applicability to those datasets generated in, e.g., meteorology, environmental science, social sciences, health-care programs, and the like. Regression methods when taxonomy variables, and when hierarchical variables, are present will also be developed. This will first be executed for classical data, and then extended to interval-valued data and to histogram- (or frequency-) valued data.With modern computers generating very large datasets, it is imperativethat techniques be developed for analysing such datasets. To date veryfew methods exist. The research will develop new methodologies foranalysing these data. A first step is to aggregate the data in somewell-defined but meaningful way. This aggregation will thence producedata in the form of lists, intervals, or distributions, and these datawill now have some form of internal structure. The research will focuson such data of two types. One will be where the data now consist ofdistributions, and where the goal is to develop methods to identify theappropraite mixture of distributions that describe these data. Anotherdeals with taxonomy and hierarical data, with the goal of establishingregression relationships that will explain the underlying processgoverning the variables involved. The resulting methodologies willallow analysis and interpretation of contemporary datastes wherecurrently no methods exist.

计算机的出现通常会带来大量非常大的数据集进行分析。 如何分析服务员数据和/或如何从这些数据中收集有用信息绝非例行公事。该提案研究了两个广泛的领域，即混合分解和存在分类和层次变量的回归。 混合分解工作涉及的数据是观测值是分布空间的 p 维笛卡尔积中的分布函数，而不是经典数据的 p 维空间中的单点。 此类数据自然产生，或者在将原始数据聚合到更易于管理的大小但保留其固有信息之后产生。目标是将这些分布划分为一致的类别并估计相关的类别分布。 建议将经典数据的联结理论的思想改编为由分布组成的数据。 这个过程中嵌入了研究参数估计的需要。 将探索不同的划分技术，例如动态聚类，将考虑不同的拟合标准度量，例如对数似然分类；以及针对底层联结和相关分布及其参数探索的不同估计方法，例如最大似然、非参数方法（例如 Parzen 截断窗口）。 由此产生的方法将广泛适用于气象学、环境科学、社会科学、医疗保健项目等中生成的数据集。 还将开发存在分类变量和层次变量时的回归方法。 这将首先针对经典数据执行，然后扩展到区间值数据和直方图（或频率）值数据。随着现代计算机生成非常大的数据集，必须开发用于分析此类数据集的技术。迄今为止，存在的方法很少。该研究将开发分析这些数据的新方法。第一步是以某种定义明确但有意义的方式聚合数据。此聚合将产生列表、区间或分布形式的数据，并且这些数据现在将具有某种形式的内部结构。该研究将重点关注两类数据。其中之一是数据现在由分布组成，目标是开发方法来识别描述这些数据的适当分布混合。另一个涉及分类法和层次数据，其目标是建立回归关系，以解释所涉及变量的基本过程。由此产生的方法将允许对目前尚无方法存在的当代数据进行分析和解释。