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Shrinkage and LASSO strategies in high-dimensional heteroscedastic models

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  • Sévérien Nkurunziza
  • Marwan Al-Momani
  • Eric Yu Yin Lin

Abstract

In this paper, we consider the estimation problem of the parameter vector in the linear regression model with heteroscedastic errors. First, under heteroscedastic errors, we study the performance of shrinkage-type estimators and their performance as compared to theunrestricted and restricted least squares estimators. In order to accommodate the heteroscedastic structure, we generalize an identity which is useful in deriving the risk function. Thanks to the established identity, we prove that shrinkage estimators dominate the unrestricted estimator. Finally, we explore the performance of high-dimensional heteroscedastic regression estimator as compared to classical LASSO and shrinkage estimators.

Suggested Citation

  • Sévérien Nkurunziza & Marwan Al-Momani & Eric Yu Yin Lin, 2016. "Shrinkage and LASSO strategies in high-dimensional heteroscedastic models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(15), pages 4454-4470, August.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:15:p:4454-4470
    DOI: 10.1080/03610926.2014.921305
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    Cited by:

    1. Marwan Al-Momani & Mohammad Arashi, 2024. "Ridge-Type Pretest and Shrinkage Estimation Strategies in Spatial Error Models with an Application to a Real Data Example," Mathematics, MDPI, vol. 12(3), pages 1-19, January.

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