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

Asar, Özgür and Ilk, Ozlem and Dag, Osman (2017) Estimating Box-Cox power transformation parameter via goodness of fit tests. Communications in Statistics – Simulation and Computation, 46 (1). pp. 91-105. ISSN 0361-0918

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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 data sets. The R package AID is proposed for implementation of the aforementioned methods.

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Journal Article
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Communications in Statistics – Simulation and Computation
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26 Aug 2014 12:27
Last Modified:
22 Nov 2022 01:04