Abstract: We show that with a class of penalty functions, numerical problems associated with the implementation of the penalized least square estimators are equivalent to the exact cover by 3-sets problem, which belongs to a class of NP-hard problems. We then extend this NP-hardness result to the cases of penalized least absolute deviation regression and penalized support vector machines. We di...

A very general mechanism for penalized regression has been added to the coxph function in S Plus A user written S Plus function can be supplied that gives addi tional term s to the partial likelihood along with the rst and second derivatives of those terms The variance and degrees of freedom for the extended model are then computed as outlined in Gray Several other arguments control optional as...