Bayesian estimation of the biasing parameter for ridge regression: A novel approach

Abstract

Multicollinearity, a common problem encountered in regression analysis, has many adverse effects on the ordinary least squares estimator. According to the literature, the ridge regression estimator is one of the useful remedies to overcome this problem. The present study is aimed to use the Bayesian approach for ridge regression and to use estimation of biasing parameters in the Bayesian paradigm by incorporating the prior information of the parameters involved. In contrary to the available Bayesian estimators, our proposed estimator permits easy computation of many posterior features of interest in regression to overcome the problem of multicollinearity. The performance of this technique has been compared with the well-known ridge regression estimators by executing an extensive simulation study. The numerical results provided an exceptional performance of the proposed technique using the mean squared error criterion. An example has been used to illustrate the proposed technique.

Keywords:

• Bayesian regression
• MCMC method
• Multicollinearity
• Posterior distribution
• Ridge regression

MSC 2020 Classification:

• 62F15
• 62J05
• 62J07