Robust inference via multiplier bootstrap
Robust inference via multiplier bootstrap
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DOI：
10.1214/19-aos1863
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发表时间：
2019-03
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通讯作者：
Xi Chen;Wen-Xin Zhou
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文献类型：
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作者：
Xi Chen;Wen-Xin Zhou
本文研究了两个基本的统计推断问题的理论基础，在重尾数据的存在下，置信集的构建和大规模的同时假设检验。对于重尾观测噪声，以样本均值为代表的最小二乘方法的有限样本性质在理论和经验上都是次优的。在本文中，我们证明了自适应Huber回归，结合乘数引导程序，提供了一个有用的鲁棒的替代最小二乘法。我们的理论和实证结果揭示了所提出的方法的有效性，并强调了具有强大的重尾推理方法的重要性。
This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With heavy-tailed observation noise, finite sample properties of the least squares-based methods, typified by the sample mean, are suboptimal both theoretically and empirically. In this paper, we demonstrate that the adaptive Huber regression, integrated with the multiplier bootstrap procedure, provides a useful robust alternative to the method of least squares. Our theoretical and empirical results reveal the effectiveness of the proposed method, and highlight the importance of having inference methods that are robust to heavy tailedness.