Statistical Methods for Models with Comstraints and Incomplete Data

NSF：DMS 9704983 模型的统计方法 约束和不完整数据 Y.Vardi和C-H Zhang罗格斯大学 摘要 问题的统计方法和推理工具 将开发不完整数据和约束参数。 主要研究课题有四个：第一个课题涉及 回归和选择偏差下的多样本数据， 取决于响应变量。一些半参数 模型（参数权重函数、非参数基分布）进行了研究，并开发了具有相关推理工具的最大似然程序。提出了在HIV临床试验中的应用。 第二个主题集中在多项模型的估计受到上限和下限的细胞概率的限制。该方法被纳入离散层析成像图像重建的EM算法。第三个专题 扩展电流 截尾截尾半参数回归模型 删失情形下的异方差回归模型 数据第四个主题集中在推理 右删失随机（增长）曲线，其中删失机制取决于曲线的进展。这是信息量大、不可验证、删失的，并且它对比较两组曲线（治疗组和对照组）的问题提出了方法学挑战。建立了基于U型统计量的曲线拟合方法，并引入半参数加速生长回归模型来拟合曲线与其对应协变量之间的关系。 该研究中心的统计方法的问题，其中数据收集是受损的抽样偏差，缺失的意见，模型与部分信息的参数。 发达 方法有助于 直接用于某些被认为具有国家战略重要性的科学领域。将约束多项式模型中单元概率估计的研究结合到电子透射层析成像二值图像的图像重建算法中; 一项重要的高科技技术，仍处于研究阶段，用于通过投影测量来估计晶体层的原子结构。 这在材料研究和制造中很重要。 半参数选择偏差模型的研究涉及到在 生物技术，因为它是在准备 用于计划中的艾滋病疫苗试验我们的目标是 分析HIV-1序列数据的方法 即将到来的疫苗试验。

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.