Moving Least Squares Regression for High-Dimensional Stochastic Simulation Metamodeling

Abstract

Simulation metamodeling is building a statistical model based on simulation output as an approximation to the system performance measure being estimated by the simulation model. In high-dimensional metamodeling problems, larger numbers of design points are needed to build an accurate and precise metamodel. Metamodeling techniques that are functions of all of these design points experience difficulties because of numerical instabilities and high computation times. We introduce a procedure to implement a local smoothing method called Moving Least Squares (MLS) regression in high-dimensional stochastic simulation metamodeling problems. Although MLS regression is known to work well when there are a very large number of design points, current procedures are focused on two- and three-dimensional cases. Furthermore, our procedure accounts for the fact that we can make replications and control the placement of design points in stochastic simulation. We provide a bound on the expected approximation error, show that the MLS predictor is consistent under certain conditions, and test the procedure with two examples that demonstrate better results than other existing simulation metamodeling techniques.