Estimating the box-cox transformation via shapiro-wilk <i>W</i> Statistic

Abstract

The Box-Cox transformation is a well known family of power transformations to bring a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Shapiro-Wilk W statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the normal based likelihood procedure and the artificial regression model procedure also presented.