Screening and Selection Methods in High-Dimensional Linear Regression Model
Screening and Selection Methods in High-Dimensional Linear Regression Model
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发表时间：
2013
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通讯作者：
Shinpei;Shota;Hirofumi
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作者：
Shinpei;Shota;Hirofumi
本文从真值模型选择和风险最小化模型选择两个角度提出了一种新的高维线性模型变量选择方法。该方法由两个因素组成：筛选和选择。这两个部分都是基于平方和的残差，这很容易理解。我们的目标是选择一个由所有非零回归系数的指数组成的模型，当真实平均结构包含在完整模型中时，称为真模型。在解释变量的约束下，使风险函数最小化。即使当目标模型的空间较大时，我们的选择方法在温和的条件下也是一致的，即目标模型的选择概率为1。此外，我们还揭示了当不能从所有可用解释变量构造真实的平均结构时，该选择方法保持了一致性。通过仿真研究表明，在各种情况下，我们的筛选和选择方法都比以往的方法更有效。AMS 2010科目分类：小学62H12；中学62J05。
In the present paper, we propose a new variable selection procedure for a high-dimensional linear model from two perspectives of the true and risk minimizing model selection. The proposed method consists of two factors: screening and selection. Both parts are based on the residual sum of squares, which can be easily understood. Our objective is to select a model consisting of indices of all nonzero regression coefficients, which is known as the true model when the true mean structure is included in the full model. Moreover, it minimizes the risk function under a restriction of explanatory variables. Even when the space of the target model is large, our selection method is consistent under mild conditions, i.e., the selection probability of the objective model goes to 1. Additionally, we reveal that consistency is retained when the true mean structure cannot be constructed from all available explanatory variables. Through simulation studies, we illustrate that our screening and selection methods are more effective than previous methods in various situations. AMS 2010 subject classifications: Primary 62H12; Secondary 62J05.