Estimating Box-Cox power transformation parameter via goodness-of-fit tests

ABSTRACT

Box–Cox power transformation is a commonly used methodology to transform the distribution of the data into a normal distribution. The methodology relies on a single transformation parameter. In this study, we focus on the estimation of this parameter. For this purpose, we employ seven popular goodness-of-fit tests for normality, namely Shapiro–Wilk, Anderson–Darling, Cramer-von Mises, Pearson Chi-square, Shapiro-Francia, Lilliefors and Jarque–Bera tests, together with a searching algorithm. The searching algorithm is based on finding the argument of the minimum or maximum depending on the test, i.e., maximum for the Shapiro–Wilk and Shapiro–Francia, minimum for the rest. The artificial covariate method of Dag et al. (2014) is also included for comparison purposes. Simulation studies are implemented to compare the performances of the methods. Results show that Shapiro–Wilk and the artificial covariate method are more effective than the others and Pearson Chi-square is the worst performing method. The methods are also applied to two real-life datasets. The R package AID is proposed for implementation of the aforementioned methods.

Keywords:

• Artificial covariate
• Data transformation
• Normality tests
• Searching algorithms
• Statistical software

Mathematics Subject Classification:

• Primary 62-07, 62F10
• Secondary 62E17, 62J05

Acknowledgment

This work received best article award among articles presented in “y-BIS 2013: Joint Meeting of Young Business and Industrial Statisticians” held on 19–21 September, 2013. We thank three anonymous Reviewers whose comments improved the presentation of this article.