MISE(p, ph) = AMISE(p, ph) + o(cid:0)(nh)−1 + h4(cid:1).

Thus if (nh)−1 → 0 and h → 0 as n → ∞, the asymptotic approximation is exact and E[(cid:15)2
These results, combined with the proof of Thm. 1 (see Appx. A.1), establish that errors of coverage, density, and convergence
all vanish in the limit. Thus E[(cid:15)2

j ] → 0 for j ∈ {1, 2, 3}, and the proof is complete.

2] → 0.

B EXPERIMENTS

Watson, Blesch, Kapar, & Wright

Our experiments do not include any personal data, as deﬁned in Article 4(1) of the European Union’s General Data Protection
Regulation. All data are either simulated or from publicly available resources. We performed all experiments on a dedicated
64-bit Linux platform running Ubuntu 20.04 with an AMD Ryzen Threadripper 3960X (24 cores, 48 threads) CPU, 256
gigabyte RAM and two NVIDIA Titan RTX GPUs. We used R version 4.1.2 and Python version 3.7.12. Further details on
the environment setup are provided in the supplemental code.
Adversarial Random Forests for Density Estimation and Generative Modeling