Bootstrap critical values for tests based on the smoothed maximum score estimator

The smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions. However, the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first-order asymptotics are used to obtain critical values. This paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values. A set of Monte Carlo experiments illustrates the numerical performance of the bootstrap.