On Prediction and the Power Transpormation Family

The power transformation family studied by Box and Cox (1964) for transforming to a normal linear model has recently been further studied by Bickel and Doksum (1978), who show that "the cost of not knowing Aand estimating it . . . is generally severe"; some of the variances for regression parameters can be extremely large. We consider prediction of future observations (untransformed) when the data can be transfo~ed to a linear model and show that while there is a cost due to estimating A it is generally not severe. Similar results emerge for the two sample problems. Monte-Carlo results lend credence to the asymptotic calculations.