Random forests for time-dependent processes

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2020-01-01 DOI:10.1051/PS/2020015

Benjamin Goehry

引用次数: 16

Abstract

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.

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时间相关过程的随机森林

布雷曼在2001年引入了随机森林。我们研究了原始布雷曼随机森林和简化版本的中心随机森林的理论方面。在独立同分布假设下，Scornet、Biau和Vert证明了Breiman随机森林的一致性，Biau研究了简化版本，得到了稀疏情况下的收敛率。然而，通常不满足i.i.d假设，例如在处理时间序列时。我们将先前的结果扩展到观测值弱依赖的情况，更准确地说，当序列是平稳的β -混合时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.