Mathematical Sciences: RUI: Semiparametric Regression Analysis

研究目标的总体主旨是为各种各样的应用和实验设计提供一种半参数替代数据分析中常用的参数回归方法。提出了离散和连续数据以及独立和相关响应的方法。目的是研究：i)解释变量离散时回归函数的非参数估计，ii)剂量反应实验中给定观测值随时间变化的剂量效应估计，以及剂量和时间之间相互作用的非参数检测，iii)条件指定分布中的估计。基于使用错误参数模型的数据分析的决策和建议是不可靠的。因此，需要发展半参数模型拟合数据的方法。本提案中概述的基础研究工作包括：i)理论工作，ii)验证程序的计算机模拟，以及iii)将半参数方法应用于弗吉尼亚联邦大学-弗吉尼亚医学院，德克萨斯大学- md安德森癌症中心和威斯康星大学麦迪逊分校眼科研究所的研究人员获得的生物医学数据。该项目还包括本科生指导和社区外展组成部分。数学科学系的本科生将协助研究项目和为埃尔帕索地区中学生设计的数学推广活动。

The overall thrust of the research objectives is to make progress towards providing, for a wide variety of applications and experimental designs, a semiparametric alternative to the popular parametric regression methods used in the analysis of data. Methodology is proposed for discrete and continuous data as well as for independent and correlated responses. The objectives are to study: i) nonparametric estimation of a regression function when the explanatory variable is discrete, ii) estimation of the dose effect given observations over time in a dose-response experiment, and nonparametric detection of interactions between dose and time, iii) estimation in conditionally specified distributions. Decisions and recommendations based on data analysis using the wrong parametric model are not reliable. Therein lies the need for the development of methodology for fitting semiparametric models to data. The basic research efforts outlined in this proposal include: i) theoretical work, ii) computer simulations to validate the procedures, and iii) application of the semiparametric methods to biomedical data obtained from researchers at Virginia Commonwealth University - Medical College of Virginia, The University of Texas - M.D. Anderson Cancer Center, and The Eye Institute of The University of Wisconsin, Madison. This project also includes an undergraduate student mentorship and community outreach component. Undergraduate students in the Department of Mathematical Sciences will assist with the research projects and with mathematics outreach activities designed for the El Paso area Middle School students.