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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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