Open Access
2024 Quantile regression by dyadic CART
Oscar Hernan Madrid Padilla, Sabyasachi Chatterjee
Author Affiliations +
Electron. J. Statist. 18(1): 1206-1247 (2024). DOI: 10.1214/24-EJS2214


In this paper we propose and study a version of the Dyadic Classification and Regression Trees (DCART) estimator from Donoho (1997) for (fixed design) quantile regression in general dimensions. We refer to this proposed estimator as the QDCART estimator. Just like the mean regression version, we show that a) a fast dynamic programming based algorithm with computational complexity O(NlogN) exists for computing the QDCART estimator and b) an oracle risk bound (trading off squared error and a complexity parameter of the true signal) holds for the QDCART estimator. This oracle risk bound then allows us to demonstrate that the QDCART estimator enjoys adaptively rate optimal estimation guarantees for piecewise constant and bounded variation function classes. In contrast to existing results for the DCART estimator which requires subgaussianity of the error distribution, for our estimation guarantees to hold we do not need any restrictive tail decay assumptions on the error distribution. For instance, our results hold even when the error distribution has no first moment such as the Cauchy distribution. Furthermore, we perform extensive numerical experiments on both simulated and real data which illustrate the usefulness of the proposed methods.


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Oscar Hernan Madrid Padilla. Sabyasachi Chatterjee. "Quantile regression by dyadic CART." Electron. J. Statist. 18 (1) 1206 - 1247, 2024.


Received: 1 June 2022; Published: 2024
First available in Project Euclid: 13 March 2024

Digital Object Identifier: 10.1214/24-EJS2214

Primary: 62G08
Secondary: 62G05

Keywords: Classification and Regression Trees (CART) , dynamic programming , piecewise constant signals , recursive dyadic partitions

Vol.18 • No. 1 • 2024
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