摘要翻译:
我们展示了Lasso估计器和Dantzig选择器之间的近似等价性。对于这两种方法,我们导出了一般非参数回归模型中预测风险的并行oracle不等式,以及当变量数远大于样本容量时线性模型中$1\lep\le2$估计损失的界。
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英文标题:
《Simultaneous analysis of Lasso and Dantzig selector》
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作者:
Peter J. Bickel, Ya'acov Ritov, and Alexandre B. Tsybakov
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最新提交年份:
2010
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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: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 exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the $\ell_p$ estimation loss for $1\le p\le 2$ in the linear model when the number of variables can be much larger than the sample size.
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PDF链接:
https://arxiv.org/pdf/801.1095