脊回归的分布Mallows模型平均

IF 0.8 3区 数学 Q2 MATHEMATICS
Haili Zhang, Alan T. K. Wan, Kang You, Guohua Zou
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引用次数: 0

摘要

岭回归是处理回归中多重共线性的有效工具。它也是收缩和正则化方法的重要类型,广泛应用于大数据和分布式数据应用中。分而治之的技巧通常应用于分布式数据,它将每个子集中的估计器与相等的权重结合在一起。为了克服多重共线性并提高分布数据存在下的估计精度,我们提出了一种用于脊回归的mallows型模型平均方法,该方法结合了来自所有子集的估计量。在允许子集数目和变量维数发散的情况下,证明了该方法是渐近最优的。所得的权估计量趋于理论最优权的一致性也得到了推导。进一步证明了模型平均估计量的渐近正态性。我们的仿真研究和实际数据分析表明,在分布式数据情况下,所提出的模型平均方法往往优于常用的模型选择和模型平均方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distributed Mallows Model Averaging for Ridge Regressions

Ridge regression is an effective tool to handle multicollinearity in regressions. It is also an essential type of shrinkage and regularization methods and is widely used in big data and distributed data applications. The divide and conquer trick, which combines the estimator in each subset with equal weight, is commonly applied in distributed data. To overcome multicollinearity and improve estimation accuracy in the presence of distributed data, we propose a Mallows-type model averaging method for ridge regressions, which combines estimators from all subsets. Our method is proved to be asymptotically optimal allowing the number of subsets and the dimension of variables to be divergent. The consistency of the resultant weight estimators tending to the theoretically optimal weights is also derived. Furthermore, the asymptotic normality of the model averaging estimator is demonstrated. Our simulation study and real data analysis show that the proposed model averaging method often performs better than commonly used model selection and model averaging methods in distributed data cases.

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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
138
审稿时长
14.5 months
期刊介绍: Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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