Regression Metamodels for Simulation with Common Random Numbers: Comparison of Techniques

摘要

Multivariate linear regression is important in many fields; in the analysis of simulation results, such a regression (meta)model may apply if common pseudorandom numbers are used. To test the validity of the specified regression model, Rao (1959) generalized the F statistic for lack of fit, whereas Kleijnen (1983) proposed cross-validation using Student's t statistic combined with Bonferroni's inequality. The paper reports on an extensive Monte Carlo experiment designed to compare these two methods. Whereas cross-validation is conservative, Rao's test realizes its nominal alpha error and has high power. Once the regression model is validated, confidence intervals for the individual regression parameters are computed. The Monte Carlo experiment compares several confidence interval procedures. For simplicity's sake, one may stick to Rao's procedure, as it has good coverage probability and acceptable halflength.