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摘要翻译：
本文在随机设计的非参数回归条件下研究了$ell_1$-惩罚最小二乘的oracle性质。我们证明了惩罚最小二乘估计满足稀疏oracle不等式，即oracle向量的非零分量个数的界。当模型维数远大于样本量，且回归矩阵不是正定的情况下，所得结果也是有效的。它们可以应用于高维线性回归、非参数自适应回归估计以及任意估计量的聚集问题。
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英文标题：
《Sparsity oracle inequalities for the Lasso》
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作者：
Florentina Bunea, Alexandre Tsybakov, Marten Wegkamp
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最新提交年份：
2007
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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：
This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. They can be applied to high-dimensional linear regression, to nonparametric adaptive regression estimation and to the problem of aggregation of arbitrary estimators.
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PDF链接：
https://arxiv.org/pdf/705.3308
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