Estimating and Validating Nonlinear Regression Metamodels in Simulation

Abstract

Frequently, the main objective of statistically designed simulation experiments is to estimate and validate regression metamodels, where the regressors are functions of the design variables and the dependent variable is the system response. In this article, a weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel is formulated and evaluated. Since the validity of a fitted regression model must be tested, a method for validating nonlinear regression simulation metamodels is presented. This method is a generalization of the cross-validation test proposed by Kleijnen (1983) in the context of linear regression metamodels. One drawback of the cross-validation strategy is the need to perform a large number of nonlinear regressions, if the number of experimental points is large. In this article, cross-validation is implemented using only one nonlinear regression. The proposed statistical analysis allows us to obtain Scheffé-type simultaneous confidence intervals for linear combinations of the metamodel's unknown parameters. Using the well-known M/M/1 example, a metamodel is built and validated with the aid of the proposed procedure.

Keywords:

• Cross-validation
• Nonlinear least squares
• Parameter estimation
• Simulation

Mathematics Subject Classification:

• Primary 93E03
• Secondary 93E24