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A Generalized Quadratic Garrote Approach Towards Ridge Regression Analysis

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Innovations in Multivariate Statistical Modeling

Abstract

Ridge regression is widely used in multiple linear regression analysis to address the prevalent multicollinearity issue in high-dimensional settings. In the standard form of ridge regression analysis, all model coefficients are shrunken towards zero at a similar rate regardless of the importance of each variable. In this paper, we provide an extension of the non-negative garrote method to give more flexibility to the ridge regression approach for unequal shrinkage of regression coefficients. We show that this approach is capable of shrinking smaller coefficients even faster than the adaptive lasso while keeping the larger coefficients almost untouched. Our generalized quadratic garrote approach enables practitioners to have more control over the amount of shrinkage on each regression coefficient estimate. We study the theoretical properties of our generalized quadratic Garrote regression estimators. Finally, we provide extensive numerical studies involving sparse, nearly sparse, and high dimensional settings and illustrate the practical use of the suggested shrinkage approach with the Boston Housing Dataset.

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Acknowledgements

Authors acknowledge the partial research support from the Natural Sciences and Engineering Research Council of Canada (NSERC). We acknowledge the reviews received by the referees.

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Correspondence to Mohammad Jafari Jozani .

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Munaweera, I., Muthukumarana, S., Jafari Jozani, M. (2022). A Generalized Quadratic Garrote Approach Towards Ridge Regression Analysis. In: Bekker, A., Ferreira, J.T., Arashi, M., Chen, DG. (eds) Innovations in Multivariate Statistical Modeling. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-031-13971-0_15

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