Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Estimating Box-Cox power transformation parameter via goodness of fit tests
AU - Asar, Özgür
AU - Ilk, Ozlem
AU - Dag, Osman
PY - 2017/1/2
Y1 - 2017/1/2
N2 - 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.
AB - 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.
KW - artificial covariate
KW - data transformation
KW - normality tests
KW - searching algorithms
KW - statistical software
U2 - 10.1080/03610918.2014.957839
DO - 10.1080/03610918.2014.957839
M3 - Journal article
VL - 46
SP - 91
EP - 105
JO - Communications in Statistics – Simulation and Computation
JF - Communications in Statistics – Simulation and Computation
SN - 0361-0918
IS - 1
ER -