arXiv 23 Sep 2023 · Econometrics · publishedEconometric Reviews (2025)
arXiv:2309.13251 · PDF · DOI · OpenAlex · Extracted main text
Considering a continuous random variable Y together with a continuous random vector X, I propose a nonparametric estimator f^(.|x) for the conditional density of Y given X=x. This estimator takes the form of an exponential series whose coefficients Tx = (Tx1,...,TxJ) are the solution of a system of nonlinear equations that depends on an estimator of the conditional expectation E[p(Y)|X=x], where p is a J-dimensional vector of basis functions. The distinguishing feature of the proposed estimator is that E[p(Y)|X=x] is estimated by generalized random forest (Athey, Tibshirani, and Wager, Annals of Statistics, 2019), targeting the heterogeneity of Tx across x. I show that f^(.|x) is uniformly consistent and asymptotically normal, allowing J to grow to infinity. I also provide a standard error formula to construct asymptotically valid confidence intervals. Results from Monte Carlo experiments are provided.
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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 | Athey, S., J. Tibshirani, and S. Wager (2019) Generalized random forests | 1.000 | 16 | 4 | 100% |
| 2 | Wu, X (2010) Exponential series estimator of multivariate densities | 0.941 | 6 | 5 | 83% |
| 3 | Wager, S. and S. Athey (2018) Estimation and inference of heterogeneous treatment effects using random forests | 0.885 | 13 | 4 | 69% |
| 4 | Barron, A. R. and C. Sheu (1991) Approximation of density functions by sequences of exponential families | 0.769 | 11 | 4 | 45% |
| 5 | Vitale, R. A (1992) Covariances of symmetric statistics | 0.737 | 4 | 3 | 50% |
| 6 | Shao, J. and C. F. J. Wu (1989) A general theory for jackknife variance estimation | 0.511 | 2 | 2 | 50% |
| 7 | van der Vaart, A. W (1998) Asymptotic Statistics | 0.511 | 2 | 2 | 50% |
| 8 | Breiman, L (2001) Random forests | 0.511 | 2 | 1 | 100% |
| 9 | Athey, S. and P. A. Haile (2007) Nonparametric approaches to auctions | 0.405 | 1 | 1 | 100% |
| 10 | Asher, S., D. Nekipelov, P. Novosad, and S. P. Ryan (2016) Classification trees for heterogeneous moment-based models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 39 scored citations.