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; 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型，非常大的数据集用于分析。 如何分析theattendant数据和/或如何从这些数据中收集有用的信息只是例行信息。该提案调查了两个广泛的领域，即分类法和分层变量的混合物分解和回归。 混合分解工作涉及数据，其中观察是分布空间的p维笛卡尔产物中的分布函数，而不是经典数据的p维空间中的单个点。 这种数据自然出现，或者在将原始数据汇总到更易于管理的大小之后，但保留其固有信息。一个目标是将这些分布分配到连贯的类中，并估算相关的类别分布。 提议将思想从Copula理论中用于经典数据，以及由分布组成的数据。 嵌入在此过程中的是需要研究参数估计。 将探讨不同的分区技术，例如动态聚类，将考虑不同的拟合标准度量，例如对数类样分类；以及针对基础Copulas及其相关分布及其参数的不同估计方法，例如最大似然，非参数方法，例如Parzen的截断窗口。 由此产生的方法将广泛适用于产生的数据集，例如气象，环境科学，社会科学，医疗保健计划等。 当分类变量和层次变量存在时，还将开发回归方法。 这将首先用于经典数据，然后将其扩展到间隔值数据和直方图 - （或频率）有价值的数据。与现代计算机生成非常大数据集的现代计算机，它是为分析此类数据集开发的不完美的技术。迄今为止存在非常富裕的方法。这项研究将开发新的方法，这些方法可以使这些数据产生影响。第一步是以某种定义但有意义的方式汇总数据。此聚合将以列表，间隔或分布的形式产生，这些汇总现在具有某种形式的内部结构。这项研究将重点的两种类型的数据。一个将是现在由分布的数据组成的地方，而目标是开发方法以识别描述这些数据的分布的及苯二颗粒混合物。另一个具有分类学和等级数据的台词，其目的是建立回归关系，以解释涉及的变量的基本处理程序。最终的方法将允许对当代数据的分析和解释，在此期间不存在任何方法。