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

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  • Özgür Asar
  • Ozlem Ilk
  • Osman Dag
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<mark>Journal publication date</mark>2/01/2017
<mark>Journal</mark>Communications in Statistics – Simulation and Computation
Issue number1
Volume46
Number of pages15
Pages (from-to)91-105
Publication StatusPublished
Early online date12/12/14
<mark>Original language</mark>English

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