Read and cite the sources.

Earlier working paper · 2018

DNN: A Two-Scale Distributional Tale of Heterogeneous Treatment Effect Inference

Yingying Fan, Jinchi Lv, and Jingbo Wang.

This earlier working paper preceded and developed into the later JASA article. It provides the earlier version of the two-scale nonparametric-inference work.

Journal of the American Statistical Association · 2024

Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors

Emre Demirkaya, Yingying Fan, Lan Gao, Jinchi Lv, Patrick Vossler, and Jingbo Wang.

119(545), 297–307. DOI: 10.1080/01621459.2022.2115375.

The article develops bias expansion, two-scale correction, asymptotic distribution theory, and resampling inference. Its supplement also addresses treatment-effect inference and technical proofs.

Management Science · forthcoming

Scalable Just-in-Time Price Elasticity Estimation

Jingbo Wang and Yufeng Huang.

The final online appendix develops uniform convergence, uniform normal approximation, derivative and quotient estimation, and bootstrap results for BNN and transformations. These are mapped to their named statements in the theory guide.

The online appendix supplied here is dated July 7, 2026. Its Section C contains the statistical results; Sections C.3–C.5 give the uniform and transformation statements, and Section C.6 contains the proofs.

Exact Bootstrap k-Nearest Neighbor Learners

B. M. Steele (2009). Machine Learning, 74(3), 235–255.

The exact nearest-neighbor averaging and rank representation precede the later inference developments.

On the Rate of Convergence of the Bagged Nearest Neighbor Estimate

Gérard Biau, Frédéric Cérou, and Arnaud Guyader (2010). Journal of Machine Learning Research, 11, 687–712.