Prediction and Power Transformations when the Choice of Power is Restricted to a Finite Set

Abstract

We study the family of power transformations proposed by Box and Cox (1964) when the choice of the power parameter λ is restricted to a finite set Ω _R . The behavior of the Box-Cox procedure is as anticipated in two extreme cases: when the true parameter λ is an element of Ω _R and when λ is “far” from Ω _R. We study the case in which λ₀ is “close” to Ω _R , finding that the resulting methods can be very different from unrestricted maximum likelihood and that inferences may depend on the design, the values of the regression parameters, and the distance of λ to Ω _R .