Total least squares and Chebyshev norm

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313045" target="_blank" >RIV/00216208:11320/15:10313045 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.procs.2015.05.393" target="_blank" >http://dx.doi.org/10.1016/j.procs.2015.05.393</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.procs.2015.05.393" target="_blank" >10.1016/j.procs.2015.05.393</a>

Result language
angličtina
Original language name
Total least squares and Chebyshev norm
Original language description
We investigate the total least square problem (TLS) with Chebyshev norm instead of the traditionally used Frobenius norm. The use of Chebyshev norm is motivated by the need for robust solutions. In order to solve the problem, we introduce interval computation and use many of the results obtained there. We show that the problem we are tackling is NP-hard in general, but it becomes polynomial in the case of a fixed number of regressors. This is the most important practical result since usually we work with regression models with a low number of regression parameters (compared to the number of observations). We present not only a precise algorithm for the problem, but also a computationally efficient heuristic. We illustrate the behavior of our method ina particular probabilistic setup by a simulation study.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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