Abstract—The ranking,problem,has become,increasingly important,in modern,applications,of statistical methods in automated decision making systems. In particular, we consider,a formulation,of the statistical ranking,problem which we call subset ranking, and focus on the DCG (discounted cumulated,gain) criterion that measures,the quality of items near,the top of the rank-list. Similar to error minimization for binary classification, direct opti- mization,of natural ranking,criteria such as DCG leads to a non-convex optimization,problems,that can be NP-hard. Therefore a computationally,more,tractable approach,is needed. We present,bounds,that relate the approximate optimization,of DCG to the approximate,minimization,of certain regression,errors. These bounds,justify the,use of convex,learning,formulations,for solving the,subset ranking,problem. The resulting estimation methods,are not conventional, in that we focus on the estimation quality in the top-portion of the rank-list. We further investigate the asymptotic,statistical behavior,of these formulations. Under appropriate conditions, the consistency of the estimation schemes,with respect to the DCG metric can be derived.