Bias and convergence rate of the coverage probability of prediction intervals in Box-Cox transformed linear models

We study the asymptotic bias and convergence rate of the coverage probability of a prediction interval in a Box-Cox transformed linear model. The leading terms in the coverage probability are obtained both when the transformation parameter is known and when it is estimated. Analytical and simulation results show that the cost of not knowing the transformation can be large in terms of coverage probability and asymptotic bias.