Rank estimators for monotonic index models

We present a new class of rank estimators of scaled coefficients in semiparametric monotonic linear index models. The estimators require no subjective bandwidth choices and have attractive computational properties. We establish √ n-consistency and asymptotic normality, and provide the general form and consistent estimators of the asymptotic covariance matrix. We also provide a generalization covering single equation multiple-indices models satisfying certain monotonicity constraints. An analogue of consistency when all explanatory variables are categorical is established, and an application is presented.