
Model Selection Criteria 147
that the statistical model
Y
j
= f (t
j
; q
0
) + E
j
, j = 1 , 2, . . . , N (4.45 )
correctly describes the observation process. In other words, (4.45) is the true
model, and q
0
is the true value of the mathematical model parameter q.
With our assumption on mea surement errors, the mathematical model pa-
rameter q can be estimated by using the ordinary least squares method; that
is, the ordinary least squa res estimator of q is obtained by solving
q
N
OLS
= arg min
q∈Ω
q
J
N
OLS
(q; Y).
Here Y = (Y
1
, Y
2
, . . . , Y
N
)
T
, and the cost function J
N
OLS
is defined as
J
N
OLS
(q; Y) =
1
N
N
X
k=1
(Y
k
− f(t
k
; q))
2
.
The corres ponding realization
ˆ
q
N
OLS
of q
N
OLS
is ...