White Noise Assumptions Revisited: Regression Models and Statistical Designs for Simulation Practice

Abstract

Classic linear regression models and their concomitant statistical designs assume a univariate response and white noise.By definition, white noise is normally, independently, and identically distributed with zero mean.This survey tries to answer the following questions: (i) How realistic are these classic assumptions in simulation practice?(ii) How can these assumptions be tested? (iii) If assumptions are violated, can the simulation's I/O data be transformed such that the assumptions hold?(iv) If not, which alternative statistical methods can then be applied?metamodels;experimental designs;generalized least squares;multivariate analysis;normality;jackknife;bootstrap;heteroscedasticity;common random numbers;validation