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.
