Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients

Hirofumi Michimae () and Takeshi Emura
Additional contact information
Hirofumi Michimae: Kitasato University
Takeshi Emura: Kurume University

Computational Statistics, 2022, vol. 37, issue 5, No 24, 2769 pages

Abstract: Abstract Ridge regression is a widely used method to mitigate the multicollinearly problem often arising in multiple linear regression. It is well known that the ridge regression estimator can be derived from the Bayesian framework by the posterior mode under a multivariate normal prior. However, the ridge regression model with a copula-based multivariate prior model has not been employed in the Bayesian framework. Motivated by the multicollinearly problem due to an interaction term, we adopt a vine copula to construct the copula-based joint prior distribution. For selected copulas and hyperparameters, we propose Bayesian ridge estimators and credible intervals for regression coefficients. A simulation study is carried out to compare the performance of four different priors (the Clayton, Gumbel, and Gaussian copula priors, and the tri-variate normal prior) on the regression coefficients. Our simulation studies demonstrate that the Archimedean (Clayton and Gumbel) copula priors give more accurate estimates in the presence of multicollinearity compared with the other priors. Finally, a real dataset is analyzed, where the Bayesian ridge estimators and some frequentist estimators are compared.

Keywords: Bayesian regression; Copula; Ridge regression; Vine copula (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s00180-022-01213-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01213-8

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-022-01213-8

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().