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型的，非常大的数据集进行分析。 如何分析伴随的数据和/或如何从这些数据中收集有用的信息是任何事情，但例行。这项建议涉及两个广泛的领域，即：混合物分解和回归分类和层次变量的存在。 混合分解工作涉及的数据中的观察是分布空间的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。 这些数据是自然产生的，或者是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的。一个目标是将这些分布划分为连贯的类，并估计相关的类分布。 它提出了适应的想法，从Copula理论的经典数据，数据组成的分布。 嵌入在这个过程中的是需要研究参数估计。 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;以及为基础Copula和相关分布及其参数探索的不同估计方法，例如，最大似然法，非参数法，如Parzen截断窗。 由此产生的方法将具有广泛的适用性，这些数据集产生的，例如，气象学、环境科学、社会科学、保健计划等。 还将开发分类变量和分层变量存在时的回归方法。 这将首先对经典数据执行，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，迫切需要开发分析此类数据集的技术。到目前为止，存在的方法很少。这项研究将开发新的方法来分析这些数据。第一步是以某种定义明确但有意义的方式聚合数据。这种聚合将产生列表、间隔或分布形式的数据，这些数据现在将具有某种形式的内部结构。研究将集中在两种类型的数据。一个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。另一个涉及分类学和层次数据，目的是建立回归关系，解释控制所涉及变量的基本过程。由此产生的方法将允许分析和解释的当代marticles wherecurrently没有方法存在。