Robust Variable Selection Based on Relaxed Lad Lasso

Least absolute deviation is proposed as a robust estimator to solve the problem when error has an asymmetric heavy-tailed distribution or outliers. In order be insensitive above situation and select truly important variables from large number of predictors in linear regression, this paper introduces two-stage variable selection method named relaxed lad lasso, which enables model obtain sparse solutions presence outliers errors by combining least with lasso. Compared not only immune rapid growth noise but also maintains better convergence rate, Opn−1/2. addition, we prove that lasso property consistency at samples; is, selects high probability one. Through simulation empirical results, further verify outstanding performance terms prediction accuracy correct informative under distribution.