A Useful Property of Best Linear Unbiased Predictors with Applications to Life-Testing

This article shows, for the Gauss–Markov model, that the best linear unbiased estimators of the model parameters remain unchanged if the predicted values of the dependent variable (based on best linear unbiased predictors) are used as observed values in estimating the parameters. This result not only provides a useful insight into the interpretation of best linear unbiased predictors, but it also simplifies calculation of predictions in some cases. We also use this result to construct large-sample approximate predictors for scale and location-scale parameter distributions. Examples from life-testing are given.