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摘要翻译：
提出了一种新的高维线性回归模型估计方法。它允许非常弱的分布假设，包括异方差性，并且不需要关于随机误差方差的知识。该方法仅基于线性规划，因此它的数值实现比已知的使用圆锥曲线程序的技术更快，并允许处理高维模型。本文给出了该估计器的估计和预测误差的上界，表明该估计器在固定设计和I.I.D.等更严格的情况下达到了相同的估计率。方差已知的高斯误差。继Gautier和Tsybakov(2011)之后，我们在比特征值限制或同化条件更弱的灵敏度假设下得到了结果。
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英文标题：
《Pivotal estimation in high-dimensional regression via linear programming》
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作者：
Eric Gautier (CREST, ENSAE), Alexandre Tsybakov (CREST, ENSAE)
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最新提交年份：
2013
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is faster than for previously known techniques using conic programs, and it allows one to deal with higher dimensional models. We provide upper bounds for estimation and prediction errors of the proposed estimator showing that it achieves the same rate as in the more restrictive situation of fixed design and i.i.d. Gaussian errors with known variance. Following Gautier and Tsybakov (2011), we obtain the results under weaker sensitivity assumptions than the restricted eigenvalue or assimilated conditions.
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PDF链接：
https://arxiv.org/pdf/1303.7092
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