Reducing bias and alleviating the influence of excess of zeros with multioutcome adaptive LAD-lasso

Zero-inflated explanatory variables are common in fields such as ecology and finance. In this paper we address the problem of having excess of zero values in some explanatory variables which are subject to multioutcome lasso-regularized variable selection. Briefly, the problem results from the failure of the lasso-type of shrinkage methods to recognize any difference between zero value occurring either in the regression coefficient or in the corresponding value of the explanatory variable. This kind of confounding will obviously increase number of false positives - all non-zero regression coefficients do not necessarily represent real outcome effects. We present here the adaptive LAD-lasso for multiple outcomes which extends the earlier work of multivariate LAD-lasso with adaptive penalization. In addition of well known property of having less biased regression coefficients, we show here how the adaptivity improves also method's ability to recover from influences of excess of zero values measured in continuous covariates.