Bayesian estimation of ridge parameter under different loss functions

In linear regression modeling, the presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). To overcome this effect, we proposed some new ridge parameters under Bayesian paradigm. Moreover, we also compare these ridge parameters with Bayesian approach under different loss functions. To access the performance of new ridge parameters, we conduct a Monte Carlo simulation study where mean squared error (MSE) is considered as an evaluation criterion. In addition, a real life example is also provided to assess the superiority of the proposed estimators on the basis of MSE and cross-validation approaches. The simulation and real application results show that the Bayesian ridge parameter estimated under Precautionary loss function is better as compared to the other loss functions as well as the MLE and ordinary ridge regression estimator.

Automated summary

In this study, new Bayesian ridge parameters are proposed to address the issue of multicollinearity in linear regression modeling. Simulation and real application results show that these new ridge parameters outperform other loss functions as well as the MLE and ordinary ridge regression estimator, particularly under the Precautionary loss function.