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Journal Articles Electronic Journal of Statistics Year : 2022

Random forest estimation of conditional distribution functions and conditional quantiles

Abstract

We propose a theoretical study of two realistic estimators of conditional distribution functions and conditional quantiles using random forests. The estimation process uses the bootstrap samples generated from the original dataset when constructing the forest. Bootstrap samples are reused to define the first estimator, while the second requires only the original sample, once the forest has been built. We prove that both proposed estimators of the conditional distribution functions are consistent uniformly a.s. To the best of our knowledge, it is the first proof of consistency including the bootstrap part. We also illustrate the estimation procedures on a numerical example.
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Dates and versions

hal-02733460 , version 1 (02-06-2020)
hal-02733460 , version 2 (11-06-2020)
hal-02733460 , version 3 (02-12-2021)
hal-02733460 , version 4 (29-08-2022)
hal-02733460 , version 5 (04-02-2023)

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Cite

Kévin Elie-Dit-Cosaque, Véronique Maume-Deschamps. Random forest estimation of conditional distribution functions and conditional quantiles. Electronic Journal of Statistics , 2022, 16 (2), ⟨10.1214/22-EJS2094⟩. ⟨hal-02733460v5⟩
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