9224544 Maxion This is the first year funding of a three-year continuing award. Discovering functional relationships among high-dimensional data is astonishingly hard. Overcoming the "curse of dimensionality" is a vital problem for any complex manufacturing industry, such as VLSI production, in which hundreds of variables must be precisely controlled in order to achieve high-quality yield. This research addresses both theoretical and practical concerns. On the theoretical end, statisticians have recently proposed a number of compelling new ideas for high-dimensional, nonparametric regression (e.g., ACE, AVAS, LOESS, PPR, MARS, RPR and several other algorithms). These ideas are largely untested, and little is known about their comparative performance in realistic situations. To remedy this, a large-scale simulation experiment is performed that employs statistical design to evaluate the effects of sample size, dimensionality, signal-to-noise ratio, and various kinds of underlying functions on the integrated mean squared error of the fitted model. The results of the study are examined in an analysis of variance, leading to clear conclusions as to the circumstances under which each of the proposed methods is most valuable. On the practical side, this research applies the methodology studied in the simulation experiment to VLSI production data as micro-modeled by the PREDITOR software, which is widely used in industry to calculate from physical principles the actual result of each step in the production of a VLSI circuit wafer. ***
