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Robust Quadratic Regression and Its Application to Energy-Growth Consumption Problem

机译:鲁棒二次回归及其在能源增长中的应用

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摘要

We propose a robust quadratic regression model to handle the statistics inaccuracy. Unlike the traditional robust statistic approaches that mainly focus on eliminating the effect of outliers, the proposed model employs the recently developed robust optimization methodology and tries to minimize the worst-case residual errors. First, we give a solvable equivalent semidefinite programming for the robust least square model with ball uncertainty set. Then the result is generalized to robust models under l_1 - and l_∞-norm critera with general ellipsoid uncertainty sets. In addition, we establish a robust regression model for per capital GDP and energy consumption in the energy-growth problem under the conservation hypothesis. Finally, numerical experiments are carried out to verify the effectiveness of the proposed models and demonstrate the effect of the uncertainty perturbation on the robust models.
机译:我们提出了一个鲁棒的二次回归模型来处理统计误差。与传统的鲁棒统计方法主要侧重于消除离群值的影响不同,所提出的模型采用了最近开发的鲁棒优化方法,并试图将最坏情况的残差最小化。首先,我们给出了具有球不确定性的鲁棒最小二乘模型的可解等效半定规划。然后将结果推广到具有一般椭球不确定性集的l_1-和l_∞-范数准则下的鲁棒模型。此外,在守恒假设下,我们针对能源增长问题中的人均GDP和能源消耗建立了鲁棒的回归模型。最后,通过数值实验验证了所提模型的有效性,并证明了不确定性扰动对鲁棒模型的影响。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第10期|210510.1-210510.10|共10页
  • 作者单位

    College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130061, China;

    Department of Automation, TNList, Tsinghua University, Beijing 100084, China;

    Development and Research Center of China Geological Survey, Beijing 100037, China;

    Development and Research Center of China Geological Survey, Beijing 100037, China,School of Earth Sciences and Resources, China University of Geosciences, Beijing 100083, China;

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