Nonparametric, isotonic discriminant procedures

In many situations it is desirable that prediction/discriminant rules should satisfy ordering properties with respect to the explanatory variables. Here, optimal rules under both L1 and L2 type loss functions are characterised under the restriction that the rules be isotonic with respect to the partial ordering on the explanatory variables. An example is given where college grade-point average is predicted based upon high school rank and American College Testing scores.