On estimating the Box-Cox transformation to normality

This paper studies four methods for estimating the Box-Cox parameter used to transform data to normality. Three of these are based on optimizing test statistics for standard normality tests (the Shapiro-Wilk, skewness, and kurtosis tests); the fourth uses the maximum likelihood estimator of the Box-Cox parameter. The four methods are compared and evaluated with a simulation study, where their performances under different skewness and kurtosis conditions are analyzed. The estimator based on optimizing the Shapiro-Wille statistic generally gives rise to the best transformations, while the maximum likelihood estimator performs almost as well. Estimators based on optimizing skewness and kurtosis do not perform well in general.