Random weighting method for smoothed binary response model

The smoothed score estimating method has the nice properties of n-consistency and asymptotic normality under some regular assumptions. However, the asymptotic variance involves quantities related to the unknown error distribution which is hard to be accurately estimated. A random weighting method for estimating the asymptotic variance of the maximum smoothed score estimators was proposed. The random weighting estimator is shown to be consistent and asymptotically normal. Statistical inference is thus possible with the variance estimates.