An Isotonic Regression Problem for Infinite-Dimensional Parameters

R. Khattree, D. P. Schmidt and I. E. Schochetman
Additional contact information
R. Khattree: Oakland University
D. P. Schmidt: Oakland University
I. E. Schochetman: Oakland University

Journal of Optimization Theory and Applications, 1999, vol. 103, issue 2, No 5, 359-384

Abstract: Abstract We consider an infinite-dimensional isotonic regression problem which is an extension of the suitably revised classical isotonic regression problem. Given p-summable data, for p finite and at least one, there exists an optimal estimator to our problem. For p greater than one, this estimator is unique and is the limit in the p-norm of the sequence of unique estimators in canonical finite-dimensional truncations of our problem. However, for p equal to one, our problem, as well as the finite-dimensional truncations, admit multiple optimal estimators in general. In this case, the sequence of optimal estimator sets to the truncations converges to the optimal estimator set of the infinite problem in the sense of Kuratowski. Moreover, the selection of natural best optimal estimators to the truncations converges in the 1-norm to an optimal estimator of the infinite problem.

Keywords: Infinite isotonic regression; optimal estimator sets; Kuratowski set convergence; natural best approximants; selection convergence (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1021704903284 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:103:y:1999:i:2:d:10.1023_a:1021704903284

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1021704903284

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().