Estimation of Linear Functionals in High Dimensional Linear Models: From Sparsity to Non-sparsity
Estimation of Linear Functionals in High Dimensional Linear Models: From Sparsity to Non-sparsity
复制标题
高维线性模型中线性泛函的估计：从稀疏到非稀疏
DOI：
10.1080/01621459.2023.2206084
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发表时间：
2023
影响因子：
3.7
通讯作者：
Liu, Yufeng
中科院分区：
文献类型：
--
作者：
Zhao, Junlong;Zhou, Yang;Liu, Yufeng
高维线性模型在实际中是常用的。在许多应用中，人们对回归系数β∈Rp的线性变换β ∈ x感兴趣，其中是一个特定的点，并且不要求与训练数据相同分布。一种常见的方法是插入技术，该技术首先估计β，然后将估计器插入线性变换中进行预测。尽管它很受欢迎，但β的估计对于高维问题可能很困难。文献中常用的假设包括系数β的信号是稀疏的，预测因子是弱相关的。然而，这些假设可能不容易验证，并且在实践中可能会被违反。当β非稀疏或预测因子强相关时，β的估计可能非常困难。在这篇文章中，我们提出了一个新的点态估计的线性变换β。这种新的估计大大放宽了高维问题的一般假设，并适应于β的稀疏程度和预测变量之间的相关强度。特别地，β可以是稀疏的或非稀疏的，并且预测因子可以是强相关的或弱相关的。该方法实现简单。数值和理论结果表明，所提出的方法在解决广泛问题方面具有竞争优势。本文的补充材料可在网上查阅。
High-dimensional linear models are commonly used in practice. In many applications, one is interested in linear transformations β⊤x of regression coefficients β∈Rp, wherexis a specific point and is not required to be identically distributed as the training data. One common approach is the plug-in technique which first estimates β, then plugs the estimator in the linear transformation for prediction. Despite its popularity, estimation of β can be difficult for high-dimensional problems. Commonly used assumptions in the literature include that the signal of coefficients β is sparse and predictors are weakly correlated. These assumptions, however, may not be easily verified, and can be violated in practice. When β is non-sparse or predictors are strongly correlated, estimation of β can be very difficult. In this article, we propose a novel pointwise estimator for linear transformations of β. This new estimator greatly relaxes the common assumptions for high-dimensional problems, and is adaptive to the degree of sparsity of β and strength of correlations among the predictors. In particular, β can be sparse or nonsparse and predictors can be strongly or weakly correlated. The proposed method is simple for implementation. Numerical and theoretical results demonstrate the competitive advantages of the proposed method for a wide range of problems. Supplementary materials for this article are available online.
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影响因子：
1.5
作者：
Belloni, Alexandre;Chernozhukov, Victor
通讯作者：
Chernozhukov, Victor
DOI：
10.1080/01621459.2017.1356319
发表时间：
2016-10
影响因子：
3.7
作者：
Yinchu Zhu;Jelena Bradic
通讯作者：
Yinchu Zhu;Jelena Bradic
通过在优化中使用随机变分不等式技术来确定套索的置信区间和区域
DOI：
--
发表时间：
2017
期刊：
影响因子：
--
作者：
Shu Lu;Yufeng Liu;Liang Yin;Kai Zhang
通讯作者：
Kai Zhang
高维回归中非稀疏系数线性投影的估计
影响因子：
1.1
作者：
David Azriel;A. Schwartzman
通讯作者：
A. Schwartzman
DOI：
10.1073/pnas.1907378117
发表时间：
2020-12-01
影响因子：
11.1
作者：
Bartlett, Peter L.;Long, Philip M.;Tsigler, Alexander
通讯作者：
Tsigler, Alexander