Statistical Methods for Models with Comstraints and Incomplete Data

美国罗格斯大学（Rutgers University） vardi y .和张c - h .摘要：研究不完全数据和约束参数问题的统计方法和推理工具。主要有四个研究主题：第一个主题涵盖了基于响应变量的选择偏差下的回归和多样本数据。研究了一些半参数模型（参数权函数、非参数基分布），并开发了具有相关推理工具的极大似然程序。提出了在HIV临床试验中的应用。第二个主题侧重于受单元概率上界和下界约束的多项模型的估计。该方法被纳入离散层析成像的EM算法中。第三个主题将目前的半参数回归模型扩展到截断-审查情况和审查数据的异方差回归模型。第四个主题集中在右截尾随机（生长）曲线的推理上，其中的截尾机制取决于曲线的进展。这是信息性的，不可忽视的，审查性的，它对比较两组曲线（处理和控制）的问题提出了方法学上的挑战。提出了基于u型统计量的方法，并引入半参数加速增长回归模型对曲线与相应协变量之间的关系进行建模。研究集中在统计方法的问题，其中的数据收集受损的抽样偏差，缺失的观测，和模型与部分信息的参数。所开发的方法直接有助于被认为具有国家战略重要性的某些科学领域。将约束多项式模型中细胞概率估计的研究纳入到电子透射断层扫描二值图像的图像重建算法中；通过投影测量来估计晶体层的原子结构是一项重要的高科技技术，目前仍处于研究阶段。这在材料研究和制造中很重要。对半参数选择偏倚模型的研究涉及生物技术的应用，因为它是为计划中的艾滋病毒疫苗试验做准备而开发的。这里的目标是找到一种方法来分析即将进行的疫苗试验中产生的HIV-1序列数据。

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.