Bayesian bootstrap adaptive lasso estimators of regression models

ABSTRACT

This paper proposes a modified adaptive lasso method by the Bayesian bootstrap (BBAL) and approximates the posterior distributions of parameters for a linear and a logistic regression model, respectively. The BBAL estimators are proved to have asymptotic and Oracle properties and they are acquired by the coordinate descent algorithm which could get the solutions at the grid of values of the penalty parameter λ. Three numerical experiments are conducted to demonstrate the BBAL method. Test results show the consistency of the variable selection and result in more robust estimators. And we use the median coefficients of the BBAL estimators to do the prediction with a medical dataset.

Keywords:

• Bayesian bootstrap
• adaptive lasso
• variable selection
• oracle properties

Disclosure statement

No potential conflict of interest was reported by the author(s).