Two-stage prediction in linear models

摘要

We consider making predictions with a fitted regression model when one of the necessary covariates is expensive, either in terms of actual cost or in terms of the effort required to collect its value. We propose a two-stage procedure that either makes the prediction without using the expensive covariate, or decides to collect the covariate and then make the prediction. The criterion for deciding whether to collect the covariate is the probability that the prediction without using the covariate is satisfactorily dose to the prediction that could be made if the covariate was collected. Three different approaches to making the prediction without using the covariate are considered. The proposed methodology is illustrated with two examples where the distributions of the covariates follow a multivariate normal distribution, and a bivariate conditional exponential distribution, respectively.