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 de…nition, 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?

Learning noise

“…Expected values of a noisy output can disguise and distort analytical structure when the system contains internal stochastic elements [5,6,9]. Noise can be multiplied into the system or pass Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”

“…Often experimental data is pre-processed to remove outliers [10], remove white noise [9], and more generally, smooth features. Common techniques for preprocessing include convolving with a low-pass-filter (e.g.…”