Robust Estimation in Binary Choice Models

The binary-response smoothed maximum score (SMS) estimator accommodates heteroskedasticity of an unknown form, but it may be heavily biased when the conditional error density is not differentiable or not bell shaped. We construct a new combined SMS estimator as a linear combination of individual estimators with weights chosen to minimize the trace of estimated mean squared error. This estimator is robust and rate-adaptive under weak assumptions on the density. Results of a Monte Carlo study confirm good performance of the combined estimator.