自回归过程中相同实现预测的数据驱动模型选择

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Kare Kamila
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引用次数: 0

摘要

本文是关于从无限阶自回归AR(\(\infty \))过程中提取的观测值的未来的一步预测。它旨在设计惩罚(完全数据驱动),确保所选模型在非渐近框架下验证效率属性。我们表明,所选择的估计器的超额风险在考虑的集合上享有最佳的偏差-方差权衡。为了获得这些结果,我们需要通过遵循经典方法来克服依赖困难,该方法包括将经验协方差矩阵限制在一个与理论协方差矩阵等效的集合中。我们用\(c_0>0\)表明该事件发生的概率大于\(1-c_0/n^2\)。建议的数据驱动标准是基于最小化的惩罚标准,类似于Mallows的\(C_p\)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Data-driven model selection for same-realization predictions in autoregressive processes

This paper is about the one-step ahead prediction of the future of observations drawn from an infinite-order autoregressive AR(\(\infty \)) process. It aims to design penalties (fully data driven) ensuring that the selected model verifies the efficiency property but in the non-asymptotic framework. We show that the excess risk of the selected estimator enjoys the best bias-variance trade-off over the considered collection. To achieve these results, we needed to overcome the dependence difficulties by following a classical approach which consists in restricting to a set where the empirical covariance matrix is equivalent to the theoretical one. We show that this event happens with probability larger than \(1-c_0/n^2\) with \(c_0>0\). The proposed data-driven criteria are based on the minimization of the penalized criterion akin to the Mallows’s \(C_p\).

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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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