Transformations of Multivariate Data

Abstract

SUMMARY Methods, which are extensions of the techniques of Box and Cox [19641, are proposed for obtaining data-based transformations of multivariate observations to enhance the normality of their distribution and also possibly to simplify the model (e.g. improve additivity, homoscedasticity, etc.). Specifically, power transformations of the original variables are estimated to effect both marginal and joint normality. A method for improving directional normality is also described. Examples are included to illustrate some properties of the methods.