Nonparametric, isotonic discriminant procedures

In many situations it is desirable that prediction/discriminant rules shoul d satisfy ordering properties with respect to the explanatory variables. He re, optimal rules under both L-1 and L-2 type loss functions are characteri sed under the restriction that the rules be isotonic with respect to the pa rtial ordering on the explanatory variables. An example is given where coll ege grade-point average is predicted based upon high school rank and Americ an College Testing scores.