Mathematical Sciences: Problems in Statistical Modeling

该项目将涉及五个统计领域的工作， 建模：（1）非参数的有效带宽选择器 局部多项式回归估计，（2）风险评估 正交表抽样，（3）质量方差模型 工程方面的改进和生产力，（4）稳健 变量误差回归;（5）自适应样条 动态规划中的近似。 首席研究员和他的研究生将 研究统计学在工程中的几个应用， 环境科学 第一个应用是对 两个量之间的关系，例如，碳百分比 在合金和硬度，当没有已知的数学 这种关系的数学形式必须是 来自数据分析。 第二是评估 环境政策的风险（比如癌症）， 相关的量（比如癌症和癌症之间的剂量反应） 戴奥辛）的含量只有不确定性。 三是设计 来学习如何减少 制造工艺。 四是在面积统计上 当某些数据需要粗略测量时， 错误-目的是识别重大错误，或至少 以消除其对估计数量的影响， 兴趣 第五是一种新的计算方法， 控制系统的最佳方法，例如，“最佳” 在需求不确定的情况下，企业的库存策略。 这里 "最佳“政策适当地平衡了超额成本 当需求超过时有销售损失的存货 库存

The project will involve work in five areas of statistical modeling: (1) efficient bandwidth selectors for nonparametric estimation by local polynomial regression, (2) risk assessment by orthogonal array sampling, (3) variance modeling for quality improvement and productivity in engineering, (4) robust regression with errors-in-variables, and (5) adaptive spline approximations in dynamic programming. The principle investigator and his graduate students will investigate several applications of statistics to engineering and environmental science. The first application is to modeling the relationship between two quantities, for example, percent carbon in an alloy and hardness, when there is no known mathematical form for this relationship so that the mathematical form must be derived from data analysis. The second is the assessment of risks (say of cancer) from environmental policies when many of the relevant quantities (say the dose response between cancer and dioxin) are known only with uncertainty. The third is the design of engineering experiments to learn how to reduce variation in manufacturing processes. The fourth is in the area statistical modeling when some of the data are subject to gross measurement errors---the object is to identify the gross errors or at least to eliminate their effect upon the estimation of quantities of interest. The fifth is a new computational method for finding the best method of controlling systems, for example, the ``best'' inventory policy for a business where demand is uncertain. Here the ``best'' policy properly balances the cost of excess inventory with the loss of sales when demand exceeds inventory.