Volume 24, 2020
|Page(s)||801 - 826|
|Published online||24 November 2020|
Random forests for time-dependent processes
Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay,
* Corresponding author: firstname.lastname@example.org
Accepted: 9 April 2020
Random forests were introduced by Breiman in 2001. We study theoretical aspects of both original Breiman’s random forests and a simplified version, the centred random forests. Under the independent and identically distributed hypothesis, Scornet, Biau and Vert proved the consistency of Breiman’s random forest, while Biau studied the simplified version and obtained a rate of convergence in the sparse case. However, the i.i.d hypothesis is generally not satisfied for example when dealing with time series. We extend the previous results to the case where observations are weakly dependent, more precisely when the sequences are stationary β−mixing.
Mathematics Subject Classification: 62M10
Key words: Statistics / random forests / time-dependent processes
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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