Skip to Main Content
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
68 Modeling and In verse Problems in the Presence of Uncertainty
θ. In [7], the almost sure convergence of J
N
OLS
(θ; Y ) to J
0
(θ) is demonstrated
constructively, that is, by building a set A F (which does not depend on
θ) with Prob{A} = 1 such that J
N
OLS
(θ; Y ) J
0
(θ) for each ω A and for
each θ
θ
. T his construction relie s upon the separability of the parameter
space
θ
(assumption (A2)) as well as the compactness of the space [t
0
, t
f
]
(assumption (A3)). The alternative a pproach of Gallant uses a consequence
of the Glivenko–Cantelli theorem [25, p. 158] to demonstrate a uniform (with
respect to θ) strong law of large numbers. The proof relies upon the dominated
conve rgence theorem [32, p. 246], and hence the dominating function b. As
a res ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Nonlinear Inverse Problems in Imaging

Nonlinear Inverse Problems in Imaging

Jin Keun Seo, Eung Je Woo
Multimodal Scene Understanding

Multimodal Scene Understanding

Michael Ying Yang, Bodo Rosenhahn, Vittorio Murino

Publisher Resources

ISBN: 9781482206432