Nonparametric estimation of conditional densities by generalized random forests
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916654746697728 |
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| author | Zincenko, Federico |
| author_facet | Zincenko, Federico |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13251 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonparametric estimation of conditional densities by generalized random forests Zincenko, Federico Econometrics 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. |
| title | Nonparametric estimation of conditional densities by generalized random forests |
| topic | Econometrics |
| url | https://arxiv.org/abs/2309.13251 |