Estimation of best predictors of binary response

This paper investigates analog estimation of predictors of binary response given semiparametric restrictions on the response process. Results are presented for the 'isotonic' response model and for the weaker 'single-crossing' model. The isotonic model assumes that the response probability is monotone in a linear function of the conditioning variables. In the single-crossing model the response probability is above a given value when a linear function of the conditioning variables is positive and below that value otherwise. It is found that analog estimators computed under the isotonicity restriction are generally consistent. Estimation under the single-crossing restriction is consistent only for special loss functions.