On prediction and the power transformation family

Abstract

The power transformation family is often used for transforming to a normal linear model. The variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated, compared to when the transformation parameter is known. We consider prediction of future untransformed observations when the data can be transformed to a linear model. When the transformation must be estimated, the prediction error is not much larger than when the parameter is known.