Proceedings of the 2006 Winter Simulation Conference
L. F. Perrone, F. P. Wieland, J. Liu, B. G. Lawson, D. M. Nicol, and R. M. Fujimoto, eds.
WHITE NOISE ASSUMPTIONS REVISITED: REGRESSION METAMODELS
AND EXPERIMENTAL DESIGNS IN PRACTICE
Jack P. C. Kleijnen
Center for Economic Research and
Department of Information Systems and Management
Tilburg University
5000 LE Tilburg, THE NETHERLANDS
ABSTRACT
Classic linear regression metamodels and their concomitant
experimental designs assume a univariate (not multivariate)
simulation response and white noise. By definition, white
noise is normally (Gaussian), independently (implying no
common random numbers), and identically (constant vari
ance) distributed with zero mean (valid metamodel). This
advanced tutorial 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 analysis becomes correct? (iv) If
such transformations cannot be applied, which alternative
statistical methods (for example, generalized least squares,
bootstrapping, jackknifing) can then be applied?
1
INTRODUCTION
Simulation models may be either deterministic or random
(stochastic). To investigate the Input/Output (I/O) behavior
of these simulation models, the analysts often use
linear
regression
metamodels; for example, firstorder and second
order polynomial approximations of the I/O function implied
by the underlying simulation model. A good analysis (for
example, a regression analysis) requires a good
statistical
design
; for example, a fractional factorial such as a
2
k

p
design.
For more mathematical details and background
information I refer to my old textbook Kleijnen (1987) and
my forthcoming textbook Kleijnen (2007); a recent tutorial
is Kleijnen (2006).
In this article, I revisit the
classic assumptions
for linear
regression analysis and its concomitant designs.
These
classic assumptions stipulate
univariate
output and
white
noise
. In practice, however, these assumptions usually do
not hold.
Indeed, in practice the simulation output (say)
hatwide
Θ
is
usually a
multivariate
random variable. For example, the
simulation output (response)
hatwide
Θ
1
may estimate the mean
flow time, and
hatwide
Θ
2
may estimate the 90% quantile of the
waiting time distribution.
More examples will follow in
Section 2.
White noise
(say)
u
is Normally, Independently, and
Identically
Distributed
(NIID)
with
zero
mean:
u
∼
NIID
(0
, σ
2
u
)
.
This definition implies the following as
sumptions:
1.
normally
(Gaussian)
distributed
simulation
re
sponses;
2.
no Common Random Numbers
(CRN) across the
(say)
n
factor (input) combinations simulated;
3.
a
common variance
(or homoscedasticity) of the
simulation responses across these
n
combinations;
4.
a
valid
regression metamodel; i.e.,
zero
expected
values for the residuals of the fitted metamodel.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 santanu
 Linear Regression, Regression Analysis, Variance, simulation output, J. P. C.

Click to edit the document details