Table 2: Simulations, Isotonic Density Estimator, 95% Confidence Intervals. (i) Panel Standard refers to standard nonparametric bootstrap, Panel m-out-of-n refers to m -out-of- n nonpara- metric bootstrap with subsample m , Panel Plug-in: ˜ V ID n refers to our proposed bootstrap-based implemented using the example-specific plug-in drift estimator, and Panel Num Deriv: ˜ V ND n refers to our proposed bootstrap-based implemented using the generic numerical derivative drift estimator. (ii) Column “ h , ϵ ” reports tuning parameter value used or average across simulations when estimated, and Columns “Coverage” and “Length” report empirical coverage and average length of bootstrap-based 95% percentile confidence intervals, respectively. (iii) h$_{MSE}$ and ϵ$_{MSE}$ correspond to the simulation MSE-optimal choices, h$_{AMSE}$ and ϵ$_{AMSE}$ correspond to the AMSE-optimal choices, and ˆ h$_{AMSE}$ and ˆ ϵ$_{AMSE}$ correspond to the ROT feasible implementation of ˆ h$_{AMSE}$ and ˆ ϵ$_{AMSE}$ described in the sup- plemental appendix. 20 Notes: (a) n = 1 , 000, S = 2 , 000, B = 2 , 000 DGP 1 DGP 2 DGP 3 h, ϵ Coverage Length h, ϵ Coverage Length h, ϵ Coverage Length Standard 0 . 828 0 . 146 0 . 808 0 . 172 0 . 821 0 . 155 m-out-of-n m = ⌈ n 1 / $^{2}$⌉ 1 . 000 0 . 438 0 . 995 0 . 495 0 . 998 0 . 452 m = n 2 / $^{3}$⌉ 0 . 989 0 . 314 0 . 979 0 . 360 0 . 989 0 . 328 m = ⌈ n 4 / $^{5}$⌉ 0 . 953 0 . 235 0 . 937 0 . 274 0 . 948 0 . 248 Plug-in: ˜ V ID n 0 . 7 · h MSE 0 . 264 0 . 955 0 . 157 0 . 202 0 . 947 0 . 183 0 . 209 0 . 957 0 . 165 0 . 8 h MSE 0 . 302 0 . 954 0 . 157 0 . 231 0 . 946 0 . 182 0 . 239 0 . 952 0 . 165 0 . 9 · h MSE 0 . 339 0 . 951 0 . 156 0 . 260 0 . 944 0 . 181 0 . 269 0 . 949 0 . 164 1 . 0 h MSE 0 . 377 0 . 949 0 . 154 0 . 289 0 . 941 0 . 180 0 . 299 0 . 948 0 . 163 1 . 1 · h MSE 0 . 415 0 . 940 0 . 151 0 . 318 0 . 938 0 . 178 0 . 329 0 . 944 0 . 161 1 . 2 h MSE 0 . 452 0 . 934 0 . 147 0 . 347 0 . 934 0 . 176 0 . 359 0 . 939 0 . 158 1 . 3 · h MSE 0 . 490 0 . 922 0 . 142 0 . 376 0 . 928 0 . 173 0 . 389 0 . 935 0 . 155 h AMSE 0 . 380 0 . 949 0 . 154 0 . 300 0 . 940 0 . 180 0 . 333 0 . 943 0 . 161 ˆ h AMSE 0 . 364 0 . 950 0 . 155 0 . 290 0 . 941 0 . 180 0 . 401 0 . 930 0 . 154 Num Deriv: ˜ V ND n 0 . 7 · ϵ MSE 0 . 726 0 . 954 0 . 158 0 . 527 0 . 947 0 . 183 0 . 554 0 . 952 0 . 165 0 . 8 ϵ MSE 0 . 830 0 . 956 0 . 159 0 . 602 0 . 947 0 . 182 0 . 633 0 . 950 0 . 164 0 . 9 · ϵ MSE 0 . 933 0 . 956 0 . 160 0 . 678 0 . 944 0 . 181 0 . 712 0 . 949 0 . 163 1 . 0 ϵ MSE 1 . 037 0 . 956 0 . 159 0 . 753 0 . 942 0 . 180 0 . 791 0 . 948 0 . 162 1 . 1 · ϵ MSE 1 . 141 0 . 955 0 . 159 0 . 828 0 . 940 0 . 179 0 . 870 0 . 946 0 . 161 1 . 2 ϵ MSE 1 . 244 0 . 956 0 . 160 0 . 904 0 . 936 0 . 177 0 . 949 0 . 943 0 . 160 1 . 3 · ϵ MSE 1 . 348 0 . 960 0 . 163 0 . 979 0 . 935 0 . 176 1 . 028 0 . 940 0 . 159 ϵ AMSE 0 . 927 0 . 956 0 . 160 0 . 731 0 . 943 0 . 180 0 . 812 0 . 948 0 . 162 ˆ ϵ AMSE 0 . 888 0 . 956 0 . 159 0 . 708 0 . 943 0 . 181 0 . 978 0 . 942 0 . 159