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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
58 Modeling and In verse Problems in the Presence of Uncertainty
We can obtain the standard errors SE
k
(
ˆ
θ
OLS
) (discussed in more detail below)
for the kth element of
ˆ
θ
OLS
by calculating SE
k
(
ˆ
θ
OLS
)
q
ˆ
Σ
N
kk
.
We note that (3.18) represents the estimate for σ
2
0
of (3.13) with the factor
1
N
replaced by the factor
1
N κ
θ
. In the linear case the estimate with
1
N
can
be shown to be biased downward (i.e., biased too low) a nd the same behavior
can be observed in the ge ne ral nonlinear case se e Chapter 12 of [35] and p.
28 of [22]. The subtraction of κ
θ
degrees of freedom reflects the fact that
ˆ
θ
has been computed to satisfy the κ
θ
normal equations (3.11). We also ...
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Publisher Resources

ISBN: 9781482206432