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Biometrika 1999 86(2):429-438; doi:10.1093/biomet/86.2.429
© 1999 by Biometrika Trust
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Nonparametric, isotonic discriminant procedures

R DykstraA1, J HewettA2 and T RobertsonA3

Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, Iowa 52242, USA A1 E-mail: dykstra@stat.uiowa.edu A3 E-mail: troberts@stat.uiowa.edu A2 Department of Statistics, University of Missouri, Columbia, Missouri 65211, USA E-mail: statjh@mizzou/.missouri.edu

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.

Key Words: Classification; Discriminant; Isotonic regression; Isotonic rule; L1 loss function; L2 loss function; Partial ordering.


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