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

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2017-01-01

Author

Asar, Ozgur
İlk Dağ, Özlem
DAĞ, OSMAN

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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 etal. (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.

Subject Keywords

Modelling and Simulation, Statistics and Probability

URI

https://hdl.handle.net/11511/34860

Journal

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION

DOI

https://doi.org/10.1080/03610918.2014.957839

Collections

Department of Statistics, Article

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Citation Formats

O. Asar, Ö. İlk Dağ, and O. DAĞ, “Estimating Box-Cox power transformation parameter via goodness-of-fit tests,” COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, pp. 91–105, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34860.