Robust Parametric Classification and Variable Selection by a Minimum   Distance Criterion
  We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, that is shrink towards the zero vector. Thus, using LASSO-like penalties to perform variable selection in the presence of outliers can result in missed detections of relevant covariates. We show that by choosing a minimum distance criterion together with an Elastic Net penalty, we can simultaneously find a parsimonious model and avoid estimation implosion even in the presence of many outliers in the important small $n$ large $p$ situation. Implementation using an MM algorithm is described and performance evaluated. 
Eric C. Chi and David W. Scott
stat.ME stat.CO stat.ML