arXiv 7 Dec 2020 · Econometrics · 1 citations (OpenAlex)
arXiv:2012.03486 · PDF · DOI · OpenAlex · Extracted main text
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this paper, we extend this result to the multivariate case and show that the vector of estimates at multiple points is jointly normal. Specifically, the covariance matrix of the limiting normal distribution is diagonal, so that the estimates at any two points are independent in sufficiently deep trees. Moreover, the off-diagonal term is bounded by quantities capturing how likely two points belong to the same partition of the resulting tree. Our results relies on certain a certain stability property when constructing splits, and we give examples of splitting rules for which this assumption is and is not satisfied. We test our proposed covariance bound and the associated coverage rates of confidence intervals in numerical simulations.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Stefan Wager and Susan Athey (2018) Estimation and inference of heterogeneous treatment effects using random forests | 1.000 | 17 | 4 | 100% |
| 2 | Stefan Wager and Guenther Walther (2015) Adaptive concentration of regression trees, with application to random forests | 0.928 | 4 | 3 | 100% |
| 3 | Tianqi Chen and Carlos Guestrin (2016) XGBoost: A scalable tree boosting system | 0.811 | 4 | 2 | 100% |
| 4 | Susan Athey, Julie Tibshirani, and Stefan Wager (2019) Generalized random forests | 0.644 | 2 | 2 | 100% |
| 5 | Xiaohui Chen (2018) Gaussian and bootstrap approximations for high-dimensional u-statistics and their applications | 0.644 | 2 | 2 | 100% |
| 6 | Victor Chernozhukov, Denis Chetverikov, and Kengo Kato (2017) Central limit theorems and bootstrap in high dimensions | 0.644 | 2 | 2 | 100% |
| 7 | Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong M… (2017) Lightgbm: A highly efficient gradient boosting decision tree | 0.644 | 2 | 2 | 100% |
| 8 | A. W. van der Vaart (1998) Asymptotic Statistics | 0.511 | 2 | 1 | 100% |
| 9 | Nino Arsov, Martin Pavlovski, and Ljupco Kocarev (2019) Stability of decision trees and logistic regression, 2019 | 0.405 | 1 | 1 | 100% |
| 10 | Patrick Billingsley (2008) Probability and measure | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 24 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Feature Selection for Personalized Policy Analysis | 0.511 | 2 | 2 |