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.

摘要

本文提出了一种改进的贝叶斯引导程序（BBAL）的自适应套索方法，并分别估计了线性和逻辑回归模型参数的后验分布。证明BBAL估计具有渐近和Oracle性质，并通过坐标下降算法获得它们，可以在惩罚参数λ的值网格上得到解。进行了三个数值实验，以证明BBAL方法。测试结果表明变量选择的一致性，并得出更可靠的估计量。并且，我们使用BBAL估计量的中位数系数对医疗数据集进行预测。