A New Type of LASSO Regression Model with Cauchy Noise

Many datasets have heavy-tailed behavior, and classical penalized models are not appropriate for them. To treat this problem, we propose a penalized regression that handles model selection and outliers issues simultaneously. We provide a LASSO regression for models with Cauchy distributed noises using the negative log-likelihood loss function. To select the regularization parameter, we define AIC and BIC type criteria. We study the distribution of the regression coefficients estimator in the simulation experiments. In addition, simulation study and real datasets analysis confirm the superiority of the proposed method.