基于指数平方损失的AR模型鲁棒变量选择

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Yaxin Wu, Yunquan Song, Xijun Liang, Yujie Gai
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引用次数: 0

摘要

时间序列分析在经济学、生态学和医学等领域有着广泛的应用。通过惩罚回归的稳健变量选择程序越来越受到关注。在我们的工作中,针对自回归(AR)模型,提出并讨论了一种基于指数平方损失的鲁棒惩罚回归估计器。具有自适应Lasso惩罚的目标模型同时实现了变量选择和参数估计。在一些正则条件下,我们建立了所提出估计量的渐近性质和“Oracle”性质。特别是,诱导的非凸不可微数学规划问题给求解算法带来了挑战。为了有效地解决这个问题,我们专门设计了一种带有凹凸过程(CCCP)的块坐标下降(BCD)算法,并提供了收敛保证。数值模拟研究表明,当存在不同类型的噪声或不同强度的噪声时,与最近的一些方法相比,该方法特别稳健和适用。此外,还对1981-1990年墨尔本日最低气温数据集进行了应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential squared loss based robust variable selection of AR models
Time series analysis is widely used in the fields of economics, ecology and medicine. Robust variable selection procedures through penalized regression have been gaining increased attention. In our work, a robust penalized regression estimator based on exponential squared loss for autoregressive (AR) models is proposed and discussed. The objective model with adaptive Lasso penalty realizes variable selection and parameter estimation simultaneously. Under some regular conditions, we establish the asymptotic and “Oracle” properties of the proposed estimator. In particular, the induced non-convex and non-differentiable mathematical programming problem offers challenges for solving algorithms. To solve this problem efficiently, we specially design a block coordinate descent (BCD) algorithm equipped with concave-convex process (CCCP) and provide a convergence guarantee. Numerical simulation studies are carried out to show that the proposed method is particularly robust and applicable compared with some recent methods when there are different types of noise or different intensity of noise. Furthermore, an application on a dataset of daily minimum temperature in Melbourne over 1981-1990 is performed.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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