UNIFORM-IN-SUBMODEL BOUNDS FOR LINEAR REGRESSION IN A MODEL-FREE FRAMEWORK
UNIFORM-IN-SUBMODEL BOUNDS FOR LINEAR REGRESSION IN A MODEL-FREE FRAMEWORK
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DOI：
10.1017/s0266466621000219
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发表时间：
2018-02
影响因子：
0.8
通讯作者：
Arun K. Kuchibhotla;L. Brown;A. Buja;E. George;Linda H. Zhao
中科院分区：
文献类型：
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作者：
Arun K. Kuchibhotla;L. Brown;A. Buja;E. George;Linda H. Zhao
在过去的二十年里，高维数据和方法在整个文献中激增。然而，线性回归的经典技术并没有失去它在应用中的有用性。事实上，许多高维估计技术可以被看作是变量选择，导致一个较小的变量集（“子模型”），其中经典的线性回归适用。我们分析线性回归估计模型选择的结果证明估计误差和线性表示界一致的子模型集。基于确定性不等式，我们的结果提供了“好”率时，适用于独立和依赖的数据。这些结果是有用的有意义的解释后，探索和减少变量的线性回归估计，也证明后模型选择的推断。所有结果都是在没有模型假设的情况下得出的，并且在性质上是非渐近的。
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.