From Fixed-X to Random-X Regression: Bias-Variance Decompositions, Covariance Penalties, and Prediction Error Estimation
从固定设计到随机设计回归:偏差方差分解、协方差惩罚与预测误差估计
In statistical prediction, classical approaches for model selection and model evaluation based on covariance penalties are still widely used. Most of the literature on this topic is based on what we call the “Fixed-X” assumption, where covariate values are assumed to be nonrandom. By contrast, it is often more reasonable to take a “Random-X” view, where the covariate values are independently drawn for both training and prediction. To study the applicability of covariance…