Estimation of the Multivariate Box-Cox Transformation Parameters

The Box-Cox transformation is a well known family of power transformations that brings a set of data closer into agreement with the normality assumption of the residuals and, hence, the response variables of a postulated model in regression analysis. This paper implements the Newton-Raphson method in estimating the multivariate Box-Cox transformation parameters and gives a new method of estimation of the parameters by maximizing the multivariate Shapiro-Wilk statistic. Simulation is performed to compare the two methods for bivariate transformations.