Adaptive Huber Regression.
Adaptive Huber Regression.
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DOI：
10.1080/01621459.2018.1543124
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发表时间：
2020
影响因子：
3.7
通讯作者：
Fan J
中科院分区：
文献类型：
--
作者：
Sun Q;Zhou WX;Fan J
大数据很容易被离群值污染或包含重型分布的变量，这使许多常规方法不足以应对这一挑战，我们提出了适应性的Huber回归。适应样本量，尺寸和矩，以在偏置和稳健性之间进行最佳权衡。低维和高维度的回归参数的估计：当δ≥1时，估算器在数据上允许下高斯型出发，而没有对数据的次级假设，而仅在0 <Δ<Δ<Δ<Δ<Δ<Δ<Δ<apter上只有较慢的率1和过渡是最佳的。所提出的方法显示出更强和预测性。
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded (1 + δ)-th moment for any δ > 0. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when δ ≥ 1, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime 0 < δ < 1 and the transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive.
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影响因子：
3.3
作者：
Landi A;Vermeire J;Iannucci V;Vanderstraeten H;Naessens E;Bentahir M;Verhasselt B
通讯作者：
Verhasselt B
DOI：
10.1111/j.1467-9868.2010.00761.x
发表时间：
2011-01-01
影响因子：
5.8
作者：
Delaigle, Aurore;Hall, Peter;Jin, Jiashun
通讯作者：
Jin, Jiashun
DOI：
10.1111/rssb.12166
发表时间：
2017-01
期刊：
Journal of the Royal Statistical Society. Series B, Statistical methodology
影响因子：
--
作者：
Fan J;Li Q;Wang Y
通讯作者：
Wang Y
影响因子：
4.5
作者：
Belloni, Alexandre;Chernozhukov, Victor
通讯作者：
Chernozhukov, Victor
影响因子：
4.5
作者：
HUBER, PJ
通讯作者：
HUBER, PJ