Robust Lasso Regression with Student-t Residuals

The lasso, introduced by Robert Tibshirani in 1996, has become one of the most popular techniques for estimating Gaussian linear regression models. An important reason for this popularity is that the lasso can simultaneously estimate all regression parameters as well as select important variables, yielding accurate regression models that are highly interpretable. This paper derives an efficient procedure for fitting robust linear regression models with the lasso in the case where the residuals are distributed according to a Student-t distribution. In contrast to Gaussian lasso regression, the proposed Student-t lasso regression procedure can be applied to data sets which contain large outlying observations. We demonstrate the utility of our Student-t lasso regression by analysing the Boston housing data set.