Least-Squares Estimation of Multifractional Random Fields in a Hilbert-Valued Context

M. D. Ruiz-Medina, V. V. Anh (), R. M. Espejo, J. M. Angulo and M. P. Frías
Additional contact information
M. D. Ruiz-Medina: University of Granada
V. V. Anh: Queensland University of Technology
R. M. Espejo: University of Granada
J. M. Angulo: University of Granada
M. P. Frías: University of Jaén

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 8, 888-911

Abstract: Abstract This paper derives conditions under which a stable solution to the least-squares linear estimation problem for multifractional random fields can be obtained. The observation model is defined in terms of a multifractional pseudodifferential equation. The weak-sense and strong-sense formulations of this problem are studied through the theory of fractional Sobolev spaces of variable order, and the spectral theory of multifractional pseudodifferential operators and their parametrix. The Theory of Reproducing Kernel Hilbert Spaces is also applied to define a stable solution to the direct and inverse estimation problems. Numerical projection methods are proposed based on the construction of orthogonal bases of these spaces. Indeed, projection into such bases leads to a regularization, removing the ill-posed nature of the estimation problem. A simulation study is developed to illustrate the estimation results derived. Some open research lines in relation to the extension of the derived results to the multifractal process context are also discussed.

Keywords: Inverse problem; Least-squares estimation; Multifractional random fields; Reproducing; Kernel Hilbert Spaces (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0423-4 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:167:y:2015:i:3:d:10.1007_s10957-013-0423-4

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

DOI: 10.1007/s10957-013-0423-4

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 ().