Robust linear regression with broad distributions of errors
Robust linear regression with broad distributions of errors
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具有广泛误差分布的稳健线性回归
DOI：
10.1016/j.physa.2015.04.025
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发表时间：
2015
影响因子：
3.3
通讯作者：
I.M. Sokolov
中科院分区：
文献类型：
--
作者：
E.B. Postnikov;I.M. Sokolov
我们考虑在随机影响（“噪声”）分布广泛（例如α稳定）的情况下噪声数据的线性拟合问题，甚至可能缺乏第一时刻。这种情况在小系统的统计物理学、地球科学、网络科学或经济物理学中很常见，不允许应用传统的高斯最大似然估计器，从而产生通常的最小二乘拟合。由于异常值的存在，这种拟合会导致拟合参数与其真实值存在较大偏差。这里讨论的方法旨在最小化残差分布的宽度。分布的相应宽度可以通过相应分布的分位数间距或通过其特征函数中的尺度参数来定义。即使在具有大异常值的短样本的情况下，该方法也能提供稳健的回归，并且等效于高斯噪声的正态最小二乘拟合。我们的讨论通过数值例子来说明。
We consider the problem of linear fitting of noisy data in the case of broad (say α-stable) distributions of random impacts (“noise”), which can lack even the first moment. This situation, common in statistical physics of small systems, in Earth sciences, in network science or in econophysics, does not allow for application of conventional Gaussian maximum-likelihood estimators resulting in usual least-squares fits. Such fits lead to large deviations of fitted parameters from their true values due to the presence of outliers. The approaches discussed here aim onto the minimization of the width of the distribution of residua. The corresponding width of the distribution can either be defined via the interquantile distance of the corresponding distributions or via the scale parameter in its characteristic function. The methods provide the robust regression even in the case of short samples with large outliers, and are equivalent to the normal least squares fit for the Gaussian noises. Our discussion is illustrated by numerical examples.
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DOI：
--
发表时间：
1970
期刊：
影响因子：
--
作者：
R. Thomas
通讯作者：
R. Thomas
影响因子：
2.4
作者：
Hu, K;Ivanov, PC;Stanley, HE
通讯作者：
Stanley, HE