Shape Restrictions, Empirical Processes, and Semiparametric Models

调查员进行研究的问题，涉及形状限制的推理，经验的过程方法和工具，以及新的理论半参数和非参数模型。特别是，调查员和华盛顿大学的研究生进行研究的凸函数估计和新的半参数模型，涉及形状限制的背景下，新的置信度设置程序。 研究者和一名华盛顿大学生物统计学研究生对具有缺失数据（通过设计）的两阶段设计的半参数模型的改进估计方法进行研究。 这项研究还涉及各种复杂的采样方法和多相设计的新的渐近理论的发展。一些关于经验过程方法和工具的研究是与荷兰的同事联合进行的。在形状约束估计下的一些推理研究是与法国、瑞士和加拿大的同事联合进行的。这些调查涉及最大似然估计，似然比统计，新的非标准极限分布的非标准渐近。 部分拟议的研究涉及更好地理解引导程序和其他在高维环境中的reservation程序。 研究还涉及基本的经验过程工具和方法的发展，以及这些新的工具和方法的应用程序有关的半参数模型，形状限制模型和高维数据的统计问题。 一个关键的目标涉及改进的经验似然理论和广义经验似然估计方法。 另一个目标是了解高维统计问题中重尾分布的影响。 应用包括高维协变量的回归模型，缺失协变量数据的生存数据模型，以及HIV-AIDS研究中使用的非参数和半参数最大似然估计。两阶段数据相关设计的工作已应用于新的设计，提高了临床试验和流行病学病例队列抽样的效率。 经验过程理论的工具允许调查的许多问题，目前的兴趣在其他领域的统计，涉及高维数据和参数空间。这项研究通过培训研究生和将由此产生的新统计方法纳入华盛顿大学统计和生物统计系的研究生课程，使教育和人类发展受益。

The investigator carries out research on problems involving shape restricted inference, empirical process methods and tools, and new theory for semiparametric and nonparametric models. In particular, the investigator and a University of Washington graduate student conduct research on new confidence set procedures in the context of convex function estimation and new semiparametric models involving shape restrictions. The investigator and a University of Washington graduate biostatistics graduate student conduct research on improved estimation methods for semiparametric models with two-phase designs with missing data (by design). This research also involves development of new asymptotic theory for a variety of complex sampling methods and multi-phase designs. Some of the research on empirical process methods and tools is carried out jointly with colleagues in the Netherlands. Some of the research on inference under shape constrained estimation is carried out jointly with colleagues in France, Switzerland, and Canada. These investigations involve nonstandard asymptotics for maximum likelihood estimators, likelihood ratio statistics, and new nonstandard limit distributions. Part of the proposed research involves better understanding of bootstrap and other resampling procedures in high-dimensional settings. The research also involves development of basic empirical process tools and methods, and applications of these new tools and methods to statistical problems concerning semiparametric models, shape restricted models, and high-dimensional data. One key goal involves improved theory for empirical likelihood and generalized empirical likelihood estimation methods. Another goal is to understand the effect of heavier tailed distributions in high-dimensional statistical problems. Applications include regression models with high-dimensional covariates, models for survival data with missing covariate data, and non- and semi-parametric maximum likelihood estimators used in HIV-AIDS research. The work on two-phase data dependent designs has application to new designs with increased efficiency for clinical trials and case-cohort sampling in epidemiology. The tools of empirical process theory allow investigations of many problems of current interest in other areas of statistics involving high-dimensional data and parameter spaces. The research benefits education and human development by the training of graduate students and the inclusion of the resulting new statistical methods in graduate level courses for the Departments of Statistics and Biostatistics at the University of Washington.