Asymptotics for high dimensional regression M-estimates: fixed design results
Asymptotics for high dimensional regression M-estimates: fixed design results
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DOI：
10.1007/s00440-017-0824-7
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发表时间：
2016-12
影响因子：
2
通讯作者：
Lihua Lei;P. Bickel;N. Karoui
中科院分区：
文献类型：
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作者：
Lihua Lei;P. Bickel;N. Karoui
研究了协变量个数与样本大小成比例增长的中值区间回归M-估计的坐标的渐近分布。在适当的正则性条件下，我们建立了固定设计矩阵下回归M-估计的坐标渐近正态。我们的证明是基于二阶Poincaré不等式和遗漏分析。一些相关的例子表明，我们的正则性条件被一类广泛的设计矩阵所满足。我们还展示了一个反例，即ANOVA类型设计，以强调技术假设不仅仅是证明的人工制品。最后，数值实验验证和补充了我们的理论结果。
We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderatep/nregime, where the number of covariatespgrows proportionally with the sample sizen. Under appropriate regularity conditions, we establish the coordinate-wise asymptotic normality of regression M-estimates assuming a fixed-design matrix. Our proof is based on the second-order Poincaré inequality and leave-one-out analysis. Some relevant examples are indicated to show that our regularity conditions are satisfied by a broad class of design matrices. We also show a counterexample, namely an ANOVA-type design, to emphasize that the technical assumptions are not just artifacts of the proof. Finally, numerical experiments confirm and complement our theoretical results.