IMPROVING THE EFFICIENCY AND ROBUSTNESS OF THE SMOOTHED MAXIMUM SCORE ESTIMATOR

Abstract

The binary-response maximum score (MS) estimator is a robust estimator, which can accommodate heteroskedasticity of an unknown form; J. Horowitz (1992) defined a smoothed maximum score estimator SMS) and demonstrated that this improves the convergence rate for sufficiently smooth conditional error densities. In this paper we relax Horowitz’s smoothness assumptions of the model and extend his asymptotic results. We also derive a joint limiting distribution of estimators with different bandwidths and smoothing kernels. We construct an estimator that combines SMS estimators for different bandwidths and kernels to overcome the uncertainty over choice of bandwidth when the degree of smoothnes of error distribution is unknown. A Monte Carlo study demonstrates the gains in efficiency and robustness.