Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00110994" target="_blank" >RIV/00216224:14310/18:00110994 - isvavai.cz</a>
Result on the web
<a href="https://www.kybernetika.cz/content/2018/5/958" target="_blank" >https://www.kybernetika.cz/content/2018/5/958</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14736/kyb-2018-5-0958" target="_blank" >10.14736/kyb-2018-5-0958</a>
Alternative languages
Result language
angličtina
Original language name
Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
Original language description
In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary test and Stein-type R-estimators uniformly. On the other hand, neither LASSO nor the usual R-estimator, preliminary test and Stein-type R-estimators outperform the other. The region of domination of LASSO over all the R-estimators (except the ridge R-estimator) is the interval around the origin of the parameter space. Finally, we observe that the L-2-risk of the restricted R-estimator equals the lower bound on the L-2-risk of LASSO. Our conclusions are based on L-2-risk analysis and relative L-2-risk efficiencies with related tables and graphs.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
KYBERNETIKA
ISSN
0023-5954
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
5
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
20
Pages from-to
958-977
UT code for WoS article
000455560300006
EID of the result in the Scopus database
2-s2.0-85064205850