A random model approach for the LASSO (Q626202)

The least absolute deviation and shrinkage operator (LASSO) method is considered for linear regression models. The authors concentrate on random effects models with Laplace distribution for the effects (unknown coefficients) where LASSO is equivalent to maximum likelihood and the choice of the regularization parameter in the LASSO penalty term can be made by the estimation of the erros and effect dispersions. An approximate marginal likelihood is derived for this estimation. A bootstrap-type procedure is described for the bias correction of the estimates. The performance of this approach and some other methods, such as cross-validation, forward and backward regression, is investigated via simulations. An application to prostate cancer data is presented.