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Penalized Regressions with Different Tuning Parameter Choosing Criteria and the Application in Economics
Sheng Gao, Mingwei Sun
Pages - 7 - 17     |    Revised - 31-07-2020     |    Published - 31-08-2020
Volume - 8   Issue - 1    |    Publication Date - August 2020  Table of Contents
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KEYWORDS
Penalized Regression, Lasso, Ridge, Elastic Net, AIC, BIC, AICc, Economic Modeling.
ABSTRACT
Recently a great deal of attention has been paid to modern regression methods such as penalized regressions which perform variable selection and coefficient estimation simultaneously, thereby providing new approaches to analyze complex data of high dimension. The choice of the tuning parameter is vital in penalized regression. In this paper, we studied the effect of different tuning parameter choosing criteria on the performances of some well-known penalization methods including ridge, lasso, and elastic net regressions. Specifically, we investigated the widely used information criteria in regression models such as Bayesian information criterion (BIC), Akaike’s information criterion (AIC), and AIC correction (AICc) in various simulation scenarios and a real data example in economic modeling. We found that predictive performance of models selected by different information criteria is heavily dependent on the properties of a data set. It is hard to find a universal best tuning parameter choosing criterion and a best penalty function for all cases. The results in this research provide reference for the choices of different criteria for tuning parameter in penalized regressions for practitioners, which also expands the nascent field of applications of penalized regressions.
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Mr. Sheng Gao
Mathematics and Computer Science Department, Samford University, Birmingham, 35229 - United States of America
Dr. Mingwei Sun
Mathematics and Computer Science Department, Samford University, Birmingham, 35229 - United States of America
msun1@samford.edu