A new Jeffrey's prior for the Box-Cox transformed linear model

Abstract

A new Jeffrey's prior for the parameters of a linear model with Box-Cox transformation (1964) is derived in this paper. Previous priors proposed by Box & Cox, Pericchi (1981), and Sweeting (1984) all assume that the prior for the power transformation parameter lamda is independent of the joint prior for the other parameters in the model. Our new prior is considered without such independence assumption, and its explicit forms are derived for one-way analysis of variances with one, two, and three populations. For one population, the new prior is identical to Sweeting's in mathematical forms, and performs better than Pericchi's as shown by simulation studies using a criterion based on the closeness of lamda posterior mode to the true value of lamda. For two and three populations, situations reverse. The new prior yields a lamda- posterior very similar to or indistinguishable from Pericchi's, and numerically performs better than Sweeting's according to the closeness criterion.