A Nonparametric Maximum Rank Correlation Estimator

This paper presents a nonparametric and distribution-free estimator for the function h*, of observable exogenous variables, x, in the generalized regression model, y - G(h*(x), mu). The method does not require a parametric specification for either the function h* or for the distribution of the random term mu. The estimation proceeds by maximizing a rank correlation criterion (Han (1987)) over a set of functions that are monotone increasing, concave, and homogeneous degree one; the function h* is assumed to belong to this set of functions. The estimator is shown to be strongly consistent.