Statistical Methods for Models with Comstraints and Incomplete Data

具有约束和不完整数据的模型的统计方法

• 批准号: 9704983
• 负责人: Yehuda Vardi
• 金额: $ 18.11万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-15 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704983&HistoricalAwards=false
• 关键词: Statistical; Methods; Models; Comstraints; Incomplete

NSF: DMS 9704983 Statistical Methods for Models with Constraints and Incomplete Data Y.Vardi and C-H Zhang Rutgers University ABSTRACT Statistical methods and inference tools for problems with incomplete - data and constrained -parameters will be developed. There are four main research topics: The first topic covers regression and multisample data under selection bias that depends on the response variable. A number of semiparametric models (parametric weight functions, nonparametric base distribution) are studied and maximum likelihood procedures with related inference tools are developed. Applications to HIV clinical trial are proposed. The second topic focuses on estimation in multinomial models subject to upper and lower bound constraints on the cell probabilities. This method is incorporated into an EM algorithm for image reconstruction in discrete tomography . The third topic extends current semiparametric regression models to truncation-censoring cases and heteroscedastic regression models with censored data. The fourth topic centers on inference for right-censored random (growth) curves, where the censoring mechanism depends on the progression of the curve. This is informative, nonignorable, censoring and it poses methodological challenges for the problems of comparing two groups of curves (treatment and control). Methodolgy based on U-type statistics is developed, and a semiparametric accelerated growth regression model is introduced to model relationship between the curves and their corresponding covariates. The research centers on statistical methods for problems in which data collection is impaired by sampling bias, missing observations, and models with partial information on the parameters. The developed methods contributes directly to certain scientific areas considered of strategic national importance. The research on estimating cell-probabilities in constrained multinomial models is incorporated in an algo rithm for image reconstruction of binary images in electron transmission tomography; an important high-tech technology, still in research stages, for estimating the atomic structure of a crystal layer by taking projection measurements. This is important in material studies and in manufacturing. The research on semiparametric selection-bias models relates to applications in biotechnology, as it is developed in preparation for planned HIV vaccine trials. The goal here, is to have a methodology in place for analyzing HIV-1 sequence data arising from forthcoming vaccine trials.

9704983带约束和不完全数据模型的统计方法。罗格斯大学，Y.Vardi，张振华，抽象统计方法和推理工具将被开发。主要研究内容有四个：第一个主题涉及选择偏倚下的回归和多样本数据，偏倚取决于响应变量。研究了几种半参数模型(参数权函数、非参数基分布)，开发了极大似然程序和相关的推理工具。提出了在HIV临床试验中的应用。第二个主题集中在单元概率的上下限约束下的多项式模型中的估计。将该方法应用于离散层析成像中的EM图像重建算法。第三个主题将现有的半参数回归模型推广到截尾截尾情形和截尾数据下的异方差回归模型。第四个主题集中于右删失随机(增长)曲线的推断，其中的审查机制取决于曲线的级数。这是一种信息性的、不可忽视的审查，它对比较两组曲线(处理和对照)的问题提出了方法学上的挑战。发展了基于U型统计的方法，并引入半参数加速增长回归模型来模拟曲线与其对应的协变量之间的关系。研究集中在针对数据收集因抽样偏差、遗漏观测和带有部分参数信息的模型而受到影响的问题的统计方法上。所开发的方法对被认为具有国家战略意义的某些科学领域有直接贡献。在约束多项式模型中估计细胞概率的研究被纳入电子透射层析成像中的二值图像重建算法中；这是一项重要的高科技技术，通过投影测量来估计晶层的原子结构，但仍处于研究阶段。这在材料研究和制造中都很重要。半参数选择-偏向模型的研究涉及到生物技术中的应用，因为它是为计划中的HIV疫苗试验而发展的。这里的目标是建立一种方法来分析来自即将到来的疫苗试验的HIV-1序列数据。