Before revision:  Finally, our testing procedure does not require any parametric assumptions on neither the outcome nor the selection equation(s) , and all our results in the conditional quantile case hold uniformly across quantile ranks in a compact set.
After revision:  Finally, our testing procedure does not require any parametric assumptions on neither the outcome nor the selection equation(s) , and all our results in the quantile case hold uniformly across quantile ranks in a compact set.