A review of ridge parameter selection: minimization of the mean squared error vs. mitigation of multicollinearity

Ridge Estimation (RE) is a widespread method to overcome the problem of collinearity defining a class of estimators depending on the non-negative scalar parameter k. A great number of papers focus on the estimation of this biasing parameter. Traditionally, the mean squared error criterion is used to...

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Bibliographic Details
Published inCommunications in statistics. Simulation and computation Vol. 53; no. 8; pp. 3686 - 3698
Main Authors García García, Catalina, Salmerón Gómez, Roman, García Pérez, José
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.08.2024
Taylor & Francis Ltd
Subjects
Collinearity
Detection
Errors
Estimation
Estimators
Mean squared error
Monte Carlo simulation
Multicollinearity
Optimization
Parameter estimation
Ridge regression
Variance inflation factor
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Summary:Ridge Estimation (RE) is a widespread method to overcome the problem of collinearity defining a class of estimators depending on the non-negative scalar parameter k. A great number of papers focus on the estimation of this biasing parameter. Traditionally, the mean squared error criterion is used to compare the performance of the different proposed estimators. However, the minimization of the mean squared error (MSE) does not always guarantee the mitigation of collinearity, meaning it is possible, for example, to obtain a variance inflation factor (VIF) higher than 10 for the k that minimizes the MSE. In this paper, we propose the VIF criteria to select the biased ridge parameter. A Monte Carlo simulation is presented with results that support this idea. Also, two real life empirical applications are used to illustrate the contribution of this paper.
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ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2022.2110594