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Lasso is a popular and efficient approach to simultaneous estimation andvariable selection in high-dimensional regression models. In this paper, arobust LAD-lasso method for multiple outcomes is presented that addresses thechallenges of non-normal outcome distributions and outlying observations.Measured covariate data from space or time, or spectral bands or genomicpositions often have natural correlation structure arising from measuringdistance between the covariates. The proposed multi-outcome approach includeshandling of such covariate blocks by a group fusion penalty, which encouragessimilarity between neighboring regression coefficient vectors by penalizingtheir differences for example in sequential data situation. Properties of theproposed approach are first illustrated by extensive simulations, and secondlythe method is applied to a real-life skewed data example on retirement behaviorwith heteroscedastic explanatory variables.

Robust multi-outcome regression with correlated covariate blocks using fused LAD-lasso