We investigate the finite sample properties of confidence intervals for f ( x 0 ) constructed using the bootstrap-based distributional approximation whose consistency was established in Theorem 3. We employ the DGPs and simulation setting previously considered in Sen, Banerjee, and Woodroofe (2010). This, as in the case of the Maximum Score estimator discussed previously, allows for a direct comparison with other bootstrap-based inference methods and their numerical performance already studied in previous work available in the literature. We estimate f ( x 0 ) at the evaluation point x 0 = 1 using a random sample of observations, where three distinct distributions are considered: DGP 1 sets x ∼ Exponential (1), DGP 2 sets x ∼ | Normal (0 , 1) | , and DGP 3 sets x ∼ |T 3 | . As in the case of the Maximum Score example, the Monte Carlo experiment employs a sample size n = 1 , 000 with B = 2 , 000 bootstrap replications and S = 2 , 000 simulations, and compares three types of bootstrap-based inference procedures: the standard non-parametric bootstrap, m -out-of- n bootstrap, and our proposed method using two distinct estimators of f $^{′}$( x 0 ) (plug-in and numerical derivative). Table 2 presents the numerical results for this example. We continue to report empirical coverage for nominal 95% confidence intervals and their average interval length. For the case of our proposed procedures, we again investigate their performance using both (i) a grid of fixed tuning parameter value (derivative step/bandwidth) and (ii) infeasible and feasible AMSE-optimal choice of tuning parameter. Also in this case, the numerical evidence is very encouraging. Our proposed bootstrap- based inference method leads to confidence intervals with excellent empirical coverage and average interval length, outperforming both the standard nonparametric bootstrap (which is inconsistent) and the m -out-of- n bootstrap (which is consistent). In particular, in this example, the plug-in method employs an off-the-shelf kernel derivative estimator, which in this case leads to confidence intervals that are very robust (i.e., insensitive) to the choice of bandwidth. Furthermore, when the corresponding feasible off-the-shelf MSE-optimal bandwidth is used, the resulting confidence intervals continue to perform excellently. Finally, the generic numerical derivative estimator also leads to very good performance of bootstrap-based infeasible and feasible confidence intervals. In sum, this example provides a second numerical illustration of the very good finite sample performance of inference based on our proposed bootstrap-based distributional approximation for cube root consistent estimators. 16