Linear Model Selection When Covariates Contain Errors
针对协变量存在测量误差时无法直接评估预测精度的问题，利用线性回归模型中的矩关系特性，提出一种模型选择方法，能渐近地选出预测误差最小的模型，对改进数据收集后的预测有用。
Prediction precision is arguably the most relevant criterion of a model in practice and is often a sought after property. A common difficulty with covariates measured with errors is the impossibility of performing prediction evaluation on the data even if a model is completely given without any unknown parameters. We bypass this inherent difficulty by using special properties on moment relations in linear regression models with measurement errors. The end product is a model selection procedure that achieves the same optimality properties that are achieved in classical linear regression models without covariate measurement error. Asymptotically, the procedure selects the model with the minimum prediction error in general, and selects the smallest correct model if the regression relation is indeed linear. Our model selection procedure is useful in prediction when future covariates without measurement error become available, e.g., due to improved technology or better management and design of data collection procedures.