Unitarily invariant errors-in-variables estimation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10329065" target="_blank" >RIV/00216208:11320/16:10329065 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007%2Fs00362-016-0800-9" target="_blank" >http://link.springer.com/article/10.1007%2Fs00362-016-0800-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00362-016-0800-9" target="_blank" >10.1007/s00362-016-0800-9</a>
Alternative languages
Result language
angličtina
Original language name
Unitarily invariant errors-in-variables estimation
Original language description
Linear relations, containing measurement errors in input and output data, are considered. Parameters of these errors-in-variables (EIV) models can be estimated by minimizing the total least squares (TLS) of the input-output disturbances, i.e., penalizing the orthogonal squared misfit. This approach corresponds to minimizing the Frobenius norm of the error matrix. An extension of the traditional TLS estimator in the EIV model - the EIV estimator - is proposed in the way that a general unitarily invariant norm of the error matrix is minimized. Such an estimator is highly non-linear. Regardless of the chosen unitarily invariant matrix norm, the corresponding EIV estimator is shown to coincide with the TLS estimator. Its existence and uniqueness is discussed. Moreover, the EIV estimator is proved to be scale invariant, interchange, direction, and rotation equivariant.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GP13-12994P" target="_blank" >GP13-12994P: Stochastic claims reserving and statistical inference in insurance</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Statistical Papers
ISSN
0932-5026
e-ISSN
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Volume of the periodical
57
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
1041-1057
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-84976475317