Rank estimation of a location parameter in the binary choice model

This paper proposes a rank-based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition, given an initial n-consistent estimator for the slope parameter. The estimator converges at the usual parametric rate. Compared with existing estimators, no nonparametric smoothing is needed here. A small Monte Carlo study illustrates the usefulness of the estimator. We also point out that the location and slope parameters can be jointly estimated.