CONTINUITY AND UNIQUENESS OF REGULARIZED OUTPUT LEAST-SQUARES OPTIMALESTIMATORS

Authors
WHITE LW ZHOU J
Citation
Lw. White et J. Zhou, CONTINUITY AND UNIQUENESS OF REGULARIZED OUTPUT LEAST-SQUARES OPTIMALESTIMATORS, Journal of mathematical analysis and applications, 196(1), 1995, pp. 53-83
Citations number
22
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications → ACNP
ISSN journal
0022247X
Volume
196
Issue
1
Year of publication
1995
Pages
53 - 83
Database
ISI
SICI code
0022-247X(1995)196:1<53:CAUORO>2.0.ZU;2-D
Abstract
The continuity and uniqueness properties of optimal estimators with re spect to data are considered for different regularizations. It is foun d that there is a weak stability for optimal estimators as set-valued mappings under a weak regularization. For stronger regularization resu lts are obtained that give stability in stronger topologies and the fi niteness of the set of optimal estimators. Finally, we give conditions that imply uniqueness of optimal estimators and Lipschitz continuity with respect to data. (C) 1995 Academic Press, Inc.