论文标题
在固定和随机设计的线性限制下选择回归模型
Selection of Regression Models under Linear Restrictions for Fixed and Random Designs
论文作者
论文摘要
线性回归中的许多重要建模任务，包括变量选择（某些预测变量的斜率等于零）和基于预测变量的总和或差异的简化模型（这些预测变量的斜率分别设置为彼此或彼此均等的斜率，或者可以将基于对调节的线性限制的基于对调节的线性限制。在本文中，我们讨论了如何使用旨在估计诸如平方误差和kullback-leibler（KL）差异的信息标准的信息标准，在存在确定性预测因子（filex-x）或随机预测变量（Random-X）的情况下。我们将现有固定X标准CP，FPE和AICC以及Random-X标准SP和RCP的理由扩展到一般线性限制。我们进一步提出并证明基于KL的标准RAICC，在Random-X下进行可变选择和一般线性限制。我们在模拟中表明，与使用基于平方错误的标准（包括交叉验证）相比，使用基于KL的标准AICC和RAICC可以提高预测性能和更稀疏的解决方案。
Many important modeling tasks in linear regression, including variable selection (in which slopes of some predictors are set equal to zero) and simplified models based on sums or differences of predictors (in which slopes of those predictors are set equal to each other, or the negative of each other, respectively), can be viewed as being based on imposing linear restrictions on regression parameters. In this paper, we discuss how such models can be compared using information criteria designed to estimate predictive measures like squared error and Kullback-Leibler (KL) discrepancy, in the presence of either deterministic predictors (fixed-X) or random predictors (random-X). We extend the justifications for existing fixed-X criteria Cp, FPE and AICc, and random-X criteria Sp and RCp, to general linear restrictions. We further propose and justify a KL-based criterion, RAICc, under random-X for variable selection and general linear restrictions. We show in simulations that the use of the KL-based criteria AICc and RAICc results in better predictive performance and sparser solutions than the use of squared error-based criteria, including cross-validation.
