Shrinkage and LASSO strategies in high-dimensional heteroscedastic models

Sévérien Nkurunziza, Marwan Al-Momani and Eric Yu Yin Lin

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 15, 4454-4470

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.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:15:p:4454-4470

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DOI: 10.1080/03610926.2014.921305

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